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MANAGEMENT SCIENCE Vol. 62, No. 6, June 2016, pp. 1778–1799 ISSN 0025-1909 (print) ó ISSN 1526-5501 (online) http://dx.doi.org/10.1287/mnsc.2015.2189 © 2016 INFORMS Optimizing Product Launches in the Presence of Strategic Consumers Ilan Lobel Leonard N. Stern School of Business, New York University, New York, New York 10012, [email protected] Jigar Patel School of Business, Montclair State University, Montclair, New Jersey 07043, [email protected] Gustavo Vulcano Leonard N. Stern School of Business, New York University, New York, New York 10012, [email protected] Jiawei Zhang Leonard N. Stern School of Business, New York University, New York, New York 10012; and New York University Shanghai, Pudong, Shanghai, China 200122, [email protected] A technology firm launches newer generations of a given product over time. At any moment, the firm decides whether to release a new version of the product that captures the current technology level at the expense of a fixed launch cost. Consumers are forward-looking and purchase newer models only when it maximizes their own future discounted surpluses. We start by assuming that consumers have a common valuation for the product and consider two product launch settings. In the first setting, the firm does not announce future release technologies and the equilibrium of the game is to release new versions cyclically with a constant level of technology improvement that is optimal for the firm. In the second setting, the firm is able to precommit to a schedule of technology releases and the optimal policy generally consists of alternating minor and major technology launch cycles. We verify that the difference in profits between the commitment and no-commitment scenarios can be significant, varying from 4% to 12%. Finally, we generalize our model to allow for multiple customer classes with different valuations for the product, demonstrating how to compute equilibria in this case and numerically deriving insights for different market compositions. Keywords : new product introduction; new product development; strategic consumer behavior; technology products; noncooperative game theory History : Received February 25, 2013; accepted November 24, 2014, by Yossi Aviv, operations management. Published online in Articles in Advance October 15, 2015. 1. Introduction Firms continuously strive to improve the products they sell to their consumers, either by enhancing the quality of their products or by incorporating new fea- tures into them. Companies take these improvements to market by releasing newer and better generations of their products over time. The cycle of firms releas- ing ever better products on the market is a particu- larly visible phenomenon in the technology industry, where companies upgrade the hardware or software they sell on a regular basis, but it is also prevalent in many other sectors of the economy where firms sell technologically enabled products to their customers, ranging from medical device manufacturers to the auto industry. A product launch is an expensive endeavor, involv- ing complex manufacturing, logistics, and marketing efforts, and a mistimed product release could have significant consequences on a firm’s profit stream (see Hendricks and Singhal 1997 and Lilien and Yoon 1990). Furthermore, firms cannot release new gener- ations of a product in rapid succession and expect consumers to willingly pay to upgrade each time a new version hits the market. A consumer will pur- chase the latest version on the market only if it is sufficiently more technologically advanced than the product he already owns. In this paper, we focus on how consumers’ forward-looking behavior affects a firm’s launch policy optimization problem. Con- sumers value newer and better technologies more than older ones and are often strategic in anticipat- ing the introduction of future generations of a prod- uct when considering purchasing the current version on the market. A properly optimized launch policy should take this behavior into account when decid- ing the appropriate time to launch new products and whether to give consumers information about upcom- ing launches. An illustrative case of consumer forward-looking behavior with respect to upcoming product launches 1778

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Page 1: MANAGEMENT SCIENCE - New York Universitypages.stern.nyu.edu/~ilobel/Product Launches.pdfLobel et al.: Optimizing Product Launches in the Presence of Strategic Consumers Management

MANAGEMENT SCIENCEVol. 62, No. 6, June 2016, pp. 1778–1799ISSN 0025-1909 (print) ó ISSN 1526-5501 (online) http://dx.doi.org/10.1287/mnsc.2015.2189

©2016 INFORMS

Optimizing Product Launches in thePresence of Strategic Consumers

Ilan LobelLeonard N. Stern School of Business, New York University, New York, New York 10012, [email protected]

Jigar PatelSchool of Business, Montclair State University, Montclair, New Jersey 07043, [email protected]

Gustavo VulcanoLeonard N. Stern School of Business, New York University, New York, New York 10012, [email protected]

Jiawei ZhangLeonard N. Stern School of Business, New York University, New York, New York 10012; and

New York University Shanghai, Pudong, Shanghai, China 200122, [email protected]

Atechnology firm launches newer generations of a given product over time. At any moment, the firm decideswhether to release a new version of the product that captures the current technology level at the expense

of a fixed launch cost. Consumers are forward-looking and purchase newer models only when it maximizestheir own future discounted surpluses. We start by assuming that consumers have a common valuation forthe product and consider two product launch settings. In the first setting, the firm does not announce futurerelease technologies and the equilibrium of the game is to release new versions cyclically with a constant levelof technology improvement that is optimal for the firm. In the second setting, the firm is able to precommitto a schedule of technology releases and the optimal policy generally consists of alternating minor and majortechnology launch cycles. We verify that the difference in profits between the commitment and no-commitmentscenarios can be significant, varying from 4% to 12%. Finally, we generalize our model to allow for multiplecustomer classes with different valuations for the product, demonstrating how to compute equilibria in this caseand numerically deriving insights for different market compositions.

Keywords : new product introduction; new product development; strategic consumer behavior; technologyproducts; noncooperative game theory

History : Received February 25, 2013; accepted November 24, 2014, by Yossi Aviv, operations management.Published online in Articles in Advance October 15, 2015.

1. IntroductionFirms continuously strive to improve the productsthey sell to their consumers, either by enhancing thequality of their products or by incorporating new fea-tures into them. Companies take these improvementsto market by releasing newer and better generationsof their products over time. The cycle of firms releas-ing ever better products on the market is a particu-larly visible phenomenon in the technology industry,where companies upgrade the hardware or softwarethey sell on a regular basis, but it is also prevalent inmany other sectors of the economy where firms selltechnologically enabled products to their customers,ranging from medical device manufacturers to theauto industry.A product launch is an expensive endeavor, involv-

ing complex manufacturing, logistics, and marketingefforts, and a mistimed product release could havesignificant consequences on a firm’s profit stream (seeHendricks and Singhal 1997 and Lilien and Yoon

1990). Furthermore, firms cannot release new gener-ations of a product in rapid succession and expectconsumers to willingly pay to upgrade each time anew version hits the market. A consumer will pur-chase the latest version on the market only if it issufficiently more technologically advanced than theproduct he already owns. In this paper, we focuson how consumers’ forward-looking behavior affectsa firm’s launch policy optimization problem. Con-sumers value newer and better technologies morethan older ones and are often strategic in anticipat-ing the introduction of future generations of a prod-uct when considering purchasing the current versionon the market. A properly optimized launch policyshould take this behavior into account when decid-ing the appropriate time to launch new products andwhether to give consumers information about upcom-ing launches.An illustrative case of consumer forward-looking

behavior with respect to upcoming product launches

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Page 2: MANAGEMENT SCIENCE - New York Universitypages.stern.nyu.edu/~ilobel/Product Launches.pdfLobel et al.: Optimizing Product Launches in the Presence of Strategic Consumers Management

Lobel et al.: Optimizing Product Launches in the Presence of Strategic ConsumersManagement Science 62(6), pp. 1778–1799, © 2016 INFORMS 1779

is the story of Apple’s iPhone. Apple Inc., the world’slargest corporation in 2014, currently earns over 50%of its revenue from iPhone sales. Since the release ofthe original iPhone in 2007, Apple has launched newgenerations of the smartphone every 12 to 16 months.Each new generation brings a more innovative designand/or better technology than its predecessor.Figure 1 shows sales data and release dates of dif-

ferent generations of the iPhone. The numbers showa significant boost in sales at the moment of launch-ing a new generation and relatively low sales in thequarter previous to a new launch. For instance, inthe third quarter of 2011, Apple sold 3 million feweriPhone 4’s than analysts had expected. At the time,Bloomberg News (Satariano 2011) argued that theupcoming launch of the newer iPhone 4S caused con-sumers to withhold their purchases and that this post-ponement behavior was the cause behind Apple’s firstmissed sales estimate in over six years. On Octo-ber 7, 2011, the iPhone 4S preorders started, andaccording to Apple, more than 4 million orders werereceived within three days, setting a record in the his-tory of mobile phone sales. This gives credence tothe claim that consumers were withholding their pur-chases until the new generation of the iPhone cameon the market. The same phenomenon occurred againin the third quarter of 2012, when earnings belowanalysts’ expectations were blamed by Apple’s chiefexecutive officer (CEO) Tim Cook (Wells 2012) on the“incredible anticipation out there for a future prod-uct,” a reference to the upcoming iPhone 5. The con-sumers, who had been holding back their smartphonepurchases, rushed to buy the iPhone 5 as soon as itcame out, and Apple reported that more than 5 mil-lion units were sold over the weekend of the product

Figure 1 (Color online) Apple iPhone Sales and Release Dates in the United States

iPhone 2G6/29/07

iPhone 3G7/11/08

iPhone 3GS6/19/09

iPhone 46/24/10

iPhone 4S10/7/11

iPhone 59/21/12

18,000Apple iPhone sales in the United States

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Notes. Data obtained from http://statista.com and http://apple.com. Note that when the release date is close to the end of a quarter, the boost in sales is alsoreflected in the next quarter.

launch. This anecdotal evidence supports the obser-vation that technology-savvy consumers look forwardand internalize the value of delaying or skipping pur-chases with the goal of maximizing the total surplusthey obtain from utilizing the firm’s products. It isalso clear, as acknowledged by Apple’s CEO, that thisstrategic behavior has a profound impact on the com-pany cash flow. How should a firm account for theconsumer strategic behavior in its launch policy tomitigate its potential negative impact? What mecha-nism can be used to deter such behavior? How muchmoney left on the table can be recovered when imple-menting such a mechanism? In this paper, we proposea stylized model to address these questions.

1.1. Overview of Main ResultsWe consider a monopolistic firm that launches suc-cessive generations of a given product, where gen-erations that are introduced later have superiortechnology and are thus more valuable to consumers.The technology process evolves according to a Brown-ian motion with a positive drift. At any point in time,there is only one product generation available in themarket, and the firm has the option to replace it witha new product generation that captures the increasedtechnology level, at the expense of incurring a fixedlaunch cost. The demand is represented by a massof infinitesimal consumers who decide which gen-erations of the product to purchase. Consumers areforward-looking and may decide to hold back theirpurchases until a newer generation of the model isreleased. In this regard, the demand for the currentgeneration model may be postponed and realized asdemand for future product generations.

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Lobel et al.: Optimizing Product Launches in the Presence of Strategic Consumers1780 Management Science 62(6), pp. 1778–1799, © 2016 INFORMS

The focus of our paper is on the characterizationof the firm’s optimal launch policy when facing sucha postponement behavior on the consumers’ side,which adds an important new dimension to the mod-els available in the literature to study the problemof optimizing new product introductions. The firmdecides the technology levels of its product releasesand does so with the objective of maximizing the netpresent value of its cash flow. Consumers similarlyoptimize their own total discounted utilities.We analyze a few variations of the general setting.

We start by assuming that consumers are homoge-neous in that they all have a common valuation forthe product and that the product price is exogenous.In the first scenario, the firm makes product launchdecisions “on the go,” as time passes and technol-ogy improves. Both the firm and the consumers makedecisions based on a Markovian state that representsthe gap between the technology the firm has devel-oped in the lab and the technology in the productcurrently available in the marketplace, as well as howoutdated the technology the consumers currently ownis. We find that in the unique equilibrium path of allMarkov perfect equilibria, the firm releases productswhenever the developed technology is better than theone available in the market by a given margin, a typeof policy we describe as the 1-cycle. In equilibrium,the firm utilizes the 1-cycle policy that maximizes itsown utility.The second scenario is one where the firm has

the ability to commit to future products’ technologylevels. The firm first preannounces technology lev-els, and the consumers follow by optimizing theirpurchasing decisions to maximize their own utilities.We characterize the firm’s optimal launch policy andthe consumers’ best response. Depending on systemparameters, the optimal launch policy is either a sin-gle introduction over the entire horizon or multiplelaunches with two alternating cycles where a smalltechnology increment is followed by a larger one,a policy we call the 2-cycle. The latter is the casefor more realistic system parameters. The rationalethat supports this strategy is that, by exercising itscommitment power, the firm can deter consumers’postponement behavior by promising a longer cycle(i.e., a major technology improvement) after two con-secutive, relatively close introductions. This releasepolicy is repeated over time and, interestingly, to acertain extent resembles Apple’s sequence of intro-ducing an iPhone with major improvements followedby an iPhone with minor changes. The iPhones 3G,4, 5, and 6 represented major redesigns of the iPhoneproduct line, whereas iPhones 3GS, 4S, 5S, and 6Scorrespond to fairly minor improvements. Depend-ing on the product and the particular launch, Appleannounces the product either several months (the

original iPhone, the Apple Watch, the Mac Pro) or afew weeks (most iPhone generations) in advance ofthe launch. Therefore, in practice, Apple utilizes anannouncing policy that is somewhere in between thetwo extreme cases that we analyze here (on the goor precommitment), but that leads to a sequence ofreleases with a similar structure to our 2-cycle, prean-nounced policy.Next, we endogenize the firm’s price and charac-

terize the joint optimal launch and pricing policy forboth scenarios. We verify that the difference in prof-its between the commitment and no-commitment sce-narios can be significant, varying from 4% to 12%depending on the problem parameters. These find-ings imply that the firm’s financial performance canbe improved if the firm is able to commit to a launchpolicy in advance. To achieve these gains, the firmdoes not need to commit to an entire launch path butonly to not releasing a new product too soon aftertwo consecutive, rather close introductions.We then generalize the special case of the model

to the multiple consumer classes that have differ-ent valuations for the product. Using a duality argu-ment, we show that the optimal launch policy underequilibrium constraints can be formulated as a singlemixed-integer program and solve the problem for dif-ferent market compositions. We also provide a recur-sive scheme for computing equilibria for the case oflaunches on the go. We find that even when launchcosts are insignificant or zero, the consumer classesare coupled, and the firm earns less revenue than itwould if it could sell to each consumer class sepa-rately. We show that the firm’s profit decreases withan increase in consumer heterogeneity. Despite theadditional complexity of the model with multiple cus-tomer classes, the output of the mixed-integer pro-gram still reflects the benefits the firm obtains fromprecommitting to the technology levels of the prod-uct launches in order to deter consumers’ speculationabout the future launch events.

1.2. OrganizationThe remainder of the paper is organized as follows:we begin with a review of the related literature inthe next section. In §3, we introduce the model witha single consumer class (i.e., consumers are homoge-neous with respect to valuations). The firm’s launchpolicy optimization problem when the firm launchesproducts on the go is analyzed in §4, followed by thecase where the firm commits to a launch policy inadvance, studied in §5. We solve the joint launch andpricing optimization problem in §6. Section 7 extendsour model to incorporate multiple consumer classes.Our concluding remarks are reported in §8. All theproofs can be found in the online appendix (avail-able as supplemental material at http://dx.doi.org/10.1287/mnsc.2015.2189).

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Lobel et al.: Optimizing Product Launches in the Presence of Strategic ConsumersManagement Science 62(6), pp. 1778–1799, © 2016 INFORMS 1781

2. Literature ReviewProduct launch policies have been explored in the op-erations management literature but usually in con-texts where demand is exogenous and treated inaggregated terms or where consumers are myopic inthe sense that they do not account for the benefit ofwaiting into their utility function.Perhaps the closest paper to ours is the work by

Krankel et al. (2006). As in our paper, they con-sider a firm that introduces successive generations ofa product over an infinite time horizon with fixedintroduction costs. In their model, the firm’s technol-ogy evolution is exogenous and stochastic, and thedemand is given by a Bass-type diffusion process.Their model leads to a trade-off similar to ours: delay-ing introduction to a later date may lead to the captureof further technology improvements, possibly at thecost of slowing sales for the existing product (and adecline in market potential for the product to be intro-duced, given their focus on durable products). Theyprove the optimality of a state-dependent thresholdpolicy that is defined based on the technology level ofthe incumbent generation, cumulative sales of the cur-rent generation, and the ongoing technology level ofthe firm’s research and development (R&D).Cohen et al. (1996) consider a finite horizon model

of product launch. They analyze the firm’s trade-offbetween the reduction of new product introductioncycle time and improvements in product perfor-mance. As in our case, their model assumes that thenewer generation replaces the previous generation.A product is introduced at the beginning of the timehorizon, and the firm needs to determine when tointroduce the new generation and what the target per-formance level should be for the new product. Theirmodel concludes that faster is not necessarily better ifthe new product market potential is large and if theexisting product (to be replaced) has a high margin.In addition, they show that it is better to take timeto develop a superior product when the firm is facedwith an intermediate level of competition.The work by Paulson Gjerde et al. (2002) con-

siders a firm’s decision-making process regardingthe level of innovation to incorporate in successiveproduct generations and discusses the frameworkunder which the firm should innovate to the tech-nology frontier compared with adopting incremen-tal improvements. Klastorin and Tsai (2004) developa game-theoretic model with two profit-maximizingfirms that enter a new market with competing prod-ucts that have finite, known life cycles. The firstentrant sets a price for its product and enjoys amonopoly situation until the second firm enters themarket. When the second firm enters the market,both firms simultaneously set (or reset) their prod-uct prices knowing the design of both products at

that time. They argue that a subgame perfect equi-librium occurs under certain conditions defined bythe parameters of the model. Their model showsthat product differentiation always arises at equi-librium because of the joint effects of resource uti-lization, price competition, and product life cycle.An important implication of their paper is that aprofit-maximizing firm would be unwise to arbitrarilyshorten its product life cycle for the sake of compe-tition. Inspired by the interactions between Intel andMicrosoft, Casadesus-Masanell and Yoffie (2007) ana-lyze a dynamic duopoly model between producers ofcomplementary products. They study the timing ofthe release of two consecutive PC generations. Theyfind that the original investments in R&D are similar,but the timing of new product releases is misaligned:Intel wants to release a new generation microproces-sor early, whereas Microsoft prefers to delay the newrelease so as to build and profit from the installedbase of the first generation.Kumar and Swaminathan (2003) consider a prod-

uct innovation problem under capacity constraints.Their model of demand, modified from the originalmodel of Bass (1969), captures the effect of unmet pastdemand on future demand. The firm’s finite produc-tion capacity plays a major role. Under this constraint,they propose a “build-up” heuristic that is a goodapproximation to the optimal policy: the firm doesnot sell for a period of time and builds up enoughinventory to never lose sales once it begins selling.The effect of environmental regulation on prod-

uct introduction policies was studied by Plambeckand Wang (2009). They consider a manufacturer whochooses the expenditure level and the developmenttime for the next product generation, which togetherdetermine its quality. Consumers purchase the newproduct and dispose of the previous generation prod-uct, which becomes e-waste. The price of a new prod-uct strictly increases with its quality, and consumersform rational expectations about the timing of thenext launch. In a monopolistic case, to maximize itsprofit, the firm introduces new products too quicklyand spends too little on R&D for each product. Asthe authors point out, if the firm could publicly com-mit to increasing the development time for the nextnew product, customers would anticipate using thecurrent new product for longer and would thereforebe willing to pay more for it. A similar result isobserved under a duopoly. The duopolists introducenew products too quickly in the sense that if theycould jointly commit to longer development times,both firms would earn greater discounted profits.Plambeck and Wang (2009) find that the firm releasesproducts at a rate that is too fast for its own profitsbut too slow for the consumers. They do not con-sider, however, the class of asymmetric launch poli-cies that the firm can utilize when it has commitment

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Lobel et al.: Optimizing Product Launches in the Presence of Strategic Consumers1782 Management Science 62(6), pp. 1778–1799, © 2016 INFORMS

power. With commitment and arbitrary launch poli-cies, we find that the firm prefers to alternate betweenminor and major launches, rather than extend thetime between launches. Even without commitment,we find a result different from Plambeck and Wang(2009), with the firm releasing products on the goat its optimal rate, which is faster than the con-sumer optimal rate. We believe this difference is dueto the distinct assumptions on the technology pro-cess. We assume the technology is given by an exoge-nous Brownian motion with a positive drift, whereasPlambeck and Wang assume technology is generatedaccording to a Cobb–Douglas production function,where a shorter development time can be compen-sated by an increased research expenditure.The problem of optimal introduction of new prod-

ucts has also been studied by the marketing com-munity. Most marketing papers build on the sem-inal work by Bass (1969) on product diffusion, byincorporating multiple product generations into theirmodels. Bayus (1992) considers two product genera-tions with overlapping diffusion of the generations.The paper analyzes the prices for the two generationsthat maximize the discounted profit after the secondproduct is launched. Norton and Bass (1987, 1992)study the substitution effect of having multiple prod-uct generations in the market simultaneously. Paeand Lehmann (2003) empirically analyze the impactof intergeneration time on product diffusion in twoindustries, random access memory chips and steel.Stremersch et al. (2010) empirically addresses thequestion of whether introducing new product gen-erations accelerates demand growth, finding that thepassage of time, not product launches, is the maindriver of demand growth. Wilson and Norton (1989)show that product line extensions should be eitherintroduced early in a product’s life cycle or not intro-duced at all, depending on the degree of substitutabil-ity between the original product and its extension.Mahajan and Muller (1996) propose an extension ofthe Bass diffusion model that captures substitutioneffects between different generations of a product. Incontrast to Wilson and Norton (1989), they find thatlaunching a new generation when the earlier productbecomes mature is sometimes the optimal strategy.There is also related work in the information sys-

tems literature about software release planning. Ruheand Saliu (2005) consider the problem of assigninga finite set of features to different software releases.Their objective is to maximize the average satisfactionof the stakeholders subject to resource and depen-dency constraints on development. The problem ismodeled as an integer programming problem, andthe solution offered is based on a linear programmingrelaxation heuristic. Greer and Ruhe (2004) consider

the release planning problem in a dynamic environ-ment, where the number of releases is not fixed.After every release, they reoptimize the problem todecide on the next release features. Another relatedproblem studied in information systems is the opti-mal bundling of information goods (see Bakos andBrynjolfsson 1999), which is a static counterpart to theproblem of optimal bundling of technologies devel-oped over time.Our work is also closely related to the economics

literature on adoption of new technologies. Balcer andLippman (1984) consider the problem of the adoptionof new technologies by a firm facing an exogenoustechnology improvement process. Similar to our opti-mal policy under no commitment, they show that thefirm will adopt the current best practice if the differ-ence between the available technology and the currenttechnology exceeds a certain threshold. They furthershow that as time passes without new technologicaladvances, it may become profitable to incorporate atechnology that has been available even though it wasnot profitable to do so in the past. Farzin et al. (1998)consider an infinite horizon dynamic programmingframework to investigate the optimal timing of tech-nology adoption. In their model, technology followsa stochastic jump process. They explicitly address theoption value of delaying adoption and compare theresults to those using traditional net present valuemethods, in which this delaying option is ignoredand technology adoption takes place as long as theresulting net cash flows are positive. They analyzeoptimal switching times to a newer technology forthe case of a single and finite known number ofswitches allowed, and they observe that the firm’soptimal timing is greatly influenced by technologicaluncertainties.Our paper contributes to the literature on forward-

looking consumers in the context of operational set-tings. Since the mid-2000s, there has been growinginterest within the revenue management commu-nity in modeling the strategic behavior of consumersand developing ways to mitigate the adverse impactof this forward-looking behavior on the firm’s rev-enues (e.g., see Aviv et al. 2009). Several of theproposed mechanisms rely on commitment devicesrelated to inventory availability and preannouncedprices (e.g., Elmaghraby et al. 2008, Aviv and Pazgal2008, Su and Zhang 2008, Correa et al. 2011, Borgset al. 2014, Besbes and Lobel 2015), using internalprice-matching policies (as in Lai et al. 2010), orusing time-binding reservations (e.g., Osadchiy andVulcano 2010). In a similar spirit to the aforemen-tioned papers, the preannouncing of launch technol-ogy levels of the successive products that we proposeserves as a commitment device that enables firms toachieve significantly more surplus compared with theon-the-go case.

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Lobel et al.: Optimizing Product Launches in the Presence of Strategic ConsumersManagement Science 62(6), pp. 1778–1799, © 2016 INFORMS 1783

3. Model3.1. DescriptionA firm continually develops technology over time.The technology developed by the firm follows astochastic process, which we assume to be a Brow-nian motion Z4t5 = åt + ëB4t5, with positive drift åand variance ë2, and where B4t5 denotes the standardBrownian motion. We represent a sample path of theBrownian motion from time 0 up until time t by ót =8Z4s52 0 s t9 2Ït and an entire sample path of theBrownian motion by ó= 8Z4s52 s � 09 2Ï.At any time t 2✓+, the firm can launch a new prod-

uct in the market with technology level Z4t5. The firmis a monopolist and chooses its launch policy to max-imize the net present value of its cash flow. Wheneverthe firm decides to launch a new product, it incursa fixed launch cost K > 0. We represent the set oftimes the firm launches new products in the marketby “ and the set of technology levels of these prod-ucts by z. Whenever the set of launch dates formsa sequence, we represent the time of the ith productrelease by íi and its technology level by zi = Z4íi5.Policies where the firm introduces only finitely manygenerations over time can also be captured by thisrepresentation by letting zj =à for some j , with theunderstanding that only jÉ1 generations of the prod-uct were available before its final disappearance fromthe marketplace.We assume that only one product generation is

available in the market at any point in time, sothe technology level introduced at time íj remainsactive during the time íj t < íj+1, and it expires attime íj+1. We denote w4t5 as the technology availablefor the consumers at time t. Formally stated,

w4t5= sup8t02“9\8t0t9

Z4t051

with the convention that w4t5= 0 for any t before thefirst product launch. We further assume that the firmhas the unlimited capacity to produce and deliver itsproduct to its customers.We assume consumers are infinitesimal and nor-

malize their mass to 1, representing each consumerby a location à in the 60117 line segment. We assumeall consumers have homogeneous preferences, with acommon valuation v, an assumption we relax in §7.Consumers are assumed to be strategic, in that theytake into account the value of delaying their purchasesand optimize their discounted total surplus over time.For any given consumer à 2 60117, we represent hisset of purchase times by  à, with the ith purchasebeing represented by äà

i , whenever the set of pur-chases forms a sequence. The set of technology lev-els of consumer à’s purchases is represented by qà,with the ith purchase having technology level qài =w4äà

i 5. We represent the technology level owned by

consumer à at time t by Cà4t5, which is equal to thetechnology available on the market at the time of thelatest purchase; i.e.,

Cà4t5= sup8t02 à9\8t0t9

w4t051

with Cà4t5= 0 at any time t before the first purchase.Whenever the consumer makes a purchase, he pays aprice p > 0 to the firm, and the firm incurs a cost c � 0to manufacture and deliver the good to the consumer.The consumer accrues utility as he uses the productover time. He does so at a higher rate when owninga technologically more advanced product. The con-sumer’s instantaneous consumption value at time tis vCà4t5; i.e., the rate is proportional to the technol-ogy he owns. We assume that both the consumers andthe firm discount the future at rate Ñ (we relax thisassumption in §7).We represent a strategy of the firm by sf 2 Sf and

a strategy of a consumer à by sà 2 Sc. We postponethe formal definition of the strategy spaces Sf and Sc

until §§4 and 5, where we study two distinct kindsof launch strategies (on the go and preannoucing,respectively) the firm might adopt. For a given strat-egy of the firm sf , the strategies of all consumers8sà

09à0 , and a sample path of the Brownian motion ó, a

consumer à’s total discounted utility U à will be equalto his discounted value obtained from using the firm’sproducts minus the payments he makes to the firm:

U à4sf 1 8sà09à01ó5=

Z à

t=0vCà4t5eÉÑt dtÉ p

àX

i=1

eÉÑäài 0

We can solve the integration in the equation aboveby noting that the technology owned by a con-sumer Cà4t5 is constant in between purchase times  à:

U à4sf 1 8sà09à01ó5

=àX

i=1

✓Z äài+1

äài

vqài eÉÑtdtÉ peÉÑäài

=àX

i=1

✓qài

✓eÉÑäài É eÉÑäài+1

◆v

ÑÉ peÉÑäài

◆0 (1)

The firm’s utility Uf is given by the total sales profitminus the launch costs; i.e.,

Uf 4sf 1 8sà09à01ó5= 4pÉ c5

Z 1

0

àX

i=1

eÉÑäài dàÉKàX

i=1

eÉÑíi 0

(2)We assume 4pÉc5>K since otherwise the firm’s opti-mal policy would be to never launch any product.As is generally done when representing random vari-ables, we will often suppress the dependence on ófrom U à and Uf . To ensure that all limits are welldefined without excessive mathematical formalism,

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Lobel et al.: Optimizing Product Launches in the Presence of Strategic Consumers1784 Management Science 62(6), pp. 1778–1799, © 2016 INFORMS

Figure 2 (Color online) Product Launches and the Consumer Utility

0 4 6 8 100

5

10

15

20

25

30

35

t

Z(t

) = !

t + "

B(t

)

z3

z2

z1

#1 #2 #3$%1 $%2

we focus on equilibria where the consumer popu-lation adopts at most finitely many different strate-gies. Given the homogeneity of the consumer market,we will focus on characterizing symmetric equilib-ria, where all consumers adopt the same strategy. Insuch situations, we will further simplify the nota-tion and represent the strategy adopted by all con-sumers by sc 2 Sc. Thus, in symmetric equilibria, thefirm’s and the consumers’ utilities will be represented,respectively, by the random variables Uf 4sf 1 sc5 andUc4sf 1 sc5.Figure 2 schematically shows the model dynam-

ics, showing a possible realization of the technologydevelopment Z4t5, the launch dates “, the launch tech-nology levels z, and the purchases of a given con-sumer à. The firm launches the first product withtechnology level z1 at time í1. This product will bein the market until time í2, which is the launch timeof the second product generation. A consumer à pur-chases this product at time äà

1; he thereafter earnsutility at a rate proportional to z1. At time í2, thefirm launches the second product generation withtechnology level z2, which replaces the first product.In the realization represented in Figure 2, the con-sumer à never purchases the second product released.The firm eventually launches the third product gen-eration with technology level z3 at time í3, which theconsumer purchases at time äà

2.

3.2. Discussion of the Model AssumptionsWhen developing our model, we deliberately simpli-fied several aspects of the problem. For example, weassume that the firm operates as a monopoly, focus-ing on the game-theoretic analysis of the interactionbetween the firm and its consumers. This is a rea-sonable assumption for settings where the firm hasa loyal customer base that prefers to buy the firm’s

product to a competitor’s. This is particularly preva-lent in markets such as the ones for smartphones,tablets, and laptop computers, where customers oftenbuy into entire product ecosystems. These ecosys-tems enable seamless integration across products andencourage customers to invest in apps that can eas-ily be ported across a firm’s product line but not to acompetitor’s product, making the true cost of switch-ing firms potentially quite high.In our model, the firm has infinite capacity. We

make this assumption since most technology firmshave sufficient initial inventory of the new product atthe launch times, or the initial high demand is satis-fied by the firm in a relatively short time frame. Forexample, despite the extremely high demand for newiPhones on launch dates, Apple has been able to sat-isfy the excess demand within a few weeks. Consid-ering that new product launches occur roughly once ayear, a few weeks is a sufficiently short response time,making it reasonable to assume that the initial highdemand is fulfilled. We make these assumptions bothfor tractability purposes and to emphasize that evenin the absence of such confounding factors, not havinga publicly announced launch policy when customersare forward-looking is potentially costly for the firm.We also assume that all product generations are sold

at the same price. Changing prices could be a riskyproposition for technology firms that seek a long-termrelationship with their customer base, as the consumeroutrage that followed the price drop of the originaliPhone less than three months after its introductionin July 2007 demonstrated. After this price imbroglioforced Apple to issue rebates to early iPhone buyers,Apple has kept the price with a service contract of thelowest storage version of its flagship phone at a con-stant US$199 in the United States, from the release ofthe iPhone 3G in 2008 at least through the launch ofthe iPhone 6 in 2014. Adner and Levinthal (2001) pro-vide good evidence that the prices of different technol-ogy product generations tend to become constant overtime. Furthermore, this assumption of fixed marginalrevenue is a commonly adopted one in the operationsliterature (see, for example, Krankel et al. 2006, Kumarand Swaminathan 2003).The modeling of the technology process as a Brown-

ian motion with positive drift captures the uncertaintyin the R&D process. The drift represents the progres-sive increment that occurs as a result of the technolog-ical investments made by the firm and its suppliers.The risk and inherent uncertainty associated with theR&D process is captured by the standard deviation.Note that though the firm faces setbacks in its tech-nology development in our model, with the Brow-nian motion moving downward as well as upward,the technology encountered by the consumer in themarketplace is always improving over time, as the

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Lobel et al.: Optimizing Product Launches in the Presence of Strategic ConsumersManagement Science 62(6), pp. 1778–1799, © 2016 INFORMS 1785

firm will never choose to launch a product that isinferior to the one it currently offers to consumers.The model also assumes the technological develop-ment occurs publicly. In reality, firms sometimes hidetheir R&D projects from consumers and competitors.The assumption of modeling the technology level asa scalar is common in the literature (see, for example,Kouvelis and Mukhopadhyay 1999, Cohen et al. 1996,Moorthy 1988, Liu and Özer 2009).Finally, in our model we assume a fixed market

size, which is normalized to have unit size. In reality,successful products tend to attract growing customerbases. We did not attempt to model the impact of alaunch policy on attracting new customers, but it isplausible that having new customers arrive over timeas a function of the technology available on the mar-ket would accentuate the firm’s incentive to introducenew products at a faster rate.

4. Launching Products On the GoIn this section, we analyze the scenario where the firmdoes not make any announcements about upcomingproduct launches and decides when to release a newproduct on the go. In practice, a firm might choose notto announce future product launches in order to main-tain operational flexibility or as an attempt to forestallconsumers from waiting until a new product comeson the market. Without a launch announcement, thefirm and the consumers play a Markov perfect equi-librium (MPE), where both sides make their decisionsbased on their beliefs about each others’ future behav-ior. An MPE is a special case of a subgame perfectequilibrium where the players make their decisionsusing Markovian strategies. Even though the playershave the option of deviating to non-Markovian strate-gies, they do not choose to do so.We consider a continuous-time formulation of the

game where the firm dynamically decides whetherto launch a new product generation or not, and con-sumers respond by deciding whether to purchase thecurrent product on the market or not. We definethe state of the game M4t5 at time t to be the pairM4t5 = 4Z4t5 É w4t51O4t55, where Z4t5 É w4t5 refersto the accumulated technology that has not yet beendeployed in a product available on the market bytime t, and O4t5 captures the aggregate outdatednessprofile of the consumers’ technology at time t. A sin-gle consumer à’s outdatedness Oà4t5 at time t is givenby Oà4t5=w4t5ÉCà4t5, which is the market technol-ogy minus the technology the consumer owns. Theoutdatedness profile O4t5 captures the fractions ofthe market with each level of outdatedness but doesnot distinguish individual customers. For example, ifw4t5= 5 and Cà4t5= 5 for all à 2 6010097, and Cà4t5= 3for all à 2 4009117, then O4t5 = 440100951 42100155, as

90% of the consumers have the most current technol-ogy on the market—an outdatedness level of zero—and 10% of the consumers have a technology that istwo units of progress behind the current one avail-able for purchase. The set of feasible values of M4t5 isdenoted by M. We consider MPEs with respect to thestate space M to ensure that the firm only respondsto the accumulated technology development and theaggregate outdatedness of the consumers, not indi-vidual consumers’ purchasing histories.At any time t 2 ✓+, the firm decides whether

to launch a new generation or not. Mathematicallyspeaking, the firm’s strategy is a mapping sf 2 M !80119 such that t 2 “ whenever sf 4M4tÉ55 = 1, whereM4tÉ5= limt0"t M4t05. That is, the firm launches a newproduct at time t depending on the state of the mar-ket at the time immediately before it, which is repre-sented by the limit tÉ in our continuous-time game.At time t, a consumer à observes the same stateas the firm, M4tÉ5, and his individual outdatednessOà4tÉ5= limt0"t Oà4t05. Formally, a consumer à’s strat-egy is sà2 M ⇥ ✓+ ! 80119, where t 2  à wheneversà4M4tÉ51Oà4tÉ55 = 1. As is standard in game the-ory, we assume the players know each other’s strate-gies. Therefore, a consumer knows when making hispurchase decision whether a launch occurs at time t,since he knows the state M4tÉ5 and, consequently,sf 4M4tÉ55.The firm and the consumers play a Markov per-

fect equilibrium 4sf 1 8sà09à05 in the following manner.

Every time a consumer makes a purchasing decision,he compares the utility from the potential purchasewith the expected utility derived from continuing touse the current product he owns. When making thischoice, he takes into account the firm’s future launchstrategy and evaluates how long he will continueusing either the current or the newly purchased prod-uct. The firm, meanwhile, also takes into account con-sumers’ purchasing strategies when deciding whetherto launch a new product. As a result, the firm will notintroduce a new product during the time in which theconsumers’ net utility from continuing the usage ofthe old product is higher than the incremental utilityfrom the new purchase. In an MPE 4sf 1 8sà

09à05, at any

state M 2M, the firm’s best response is to play accord-ing to sf , assuming the consumers will play accordingto 8sà

09à0 in the future, and at any state M 2 M and

outdatedness Oà 2 ✓+, a consumer à’s best responseis to play according to sà, assuming the firm will playaccording to sf in the future and the other consumerswill act according to 8sà

09à0 6=à now and in the future.

To analyze the MPE of this game, we first focus onthe consumer best response. Suppose the firm utilizesa simple threshold strategy where it launches a newproduct whenever Z4t5Éw4t5� z for some thresholdvalue z > 0. That is, if the technology available in the

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Lobel et al.: Optimizing Product Launches in the Presence of Strategic Consumers1786 Management Science 62(6), pp. 1778–1799, © 2016 INFORMS

lab is sufficiently better than the technology availablein the market, the firm releases a new product. Nat-urally, if z is large, the consumers will respond bybuying every time there is a new release, but con-sumers will prefer to skip generations of the productif z is close to zero. The following lemma character-izes the lowest threshold z at which consumers buyall products released by the firm.

Lemma 1. Assume the firm releases a new productwhenever Z4t5Éw4t5� z for some threshold z� 0. Then,consumers will purchase every release if and only if z� z⇤,where z⇤ is the unique positive solution of the equation

z41É eÉ„z5= pÑ

v(3)

and „ is the technology-dependent discount rate

„= 2Ñpå2 + 2Ñë2 +å

0 (4)

Equation (3) determines the threshold policy thatleads consumers to become indifferent to any singlepurchase. To be clear, consumers still earn positiveutility from their overall interactions with the firmwhenever the products released exhibit an improve-ment of z⇤; only the marginal purchase yields zeroexpected utility for the consumer under this releasepolicy, in the sense that if the consumer were to skipone product launch, he would not lose any utility,but if he skipped two consecutive launches, he wouldearn a strictly lower utility. In Equation (3), the factthat consumers anticipate future upgrades when con-sidering purchasing today appears in the formula asthe term eÉ„z.The parameter „, which we call the technology-

dependent discount rate, is defined based on both thediscount rate Ñ and the parameters of the Brownianmotion Z4t5. Naturally, the term „ is increasing in Ñand decreasing in å, as both increasing the discountrate or decreasing the positive drift of the technolog-ical progress makes the future releases less valuabletoday. Surprisingly, the term „ is decreasing in thevariance ë2 of the technology Brownian motion. Thisimplies that a more predictable technological processmakes future technology less valuable in expectation.This is a consequence of the fact that launching anew product is a real option for the firm, as it willonly release new products after technological progressis achieved, never after a technological setback. Theinteresting implication is that the firm does not face atrade-off between the drift å and the variance ë2 and,in fact, should be willing to invest in order to increaseboth parameters.We now turn to our main result in this section,

where we show the unique equilibrium path of anyMPE of the game being played by the firm and theconsumers.

Theorem 1. In the equilibrium path of any MPE, prod-uct launches occur exclusively when Z4t5 É w4t5 = z⇤,where z⇤ is defined in Equation (3). Furthermore, all con-sumers (except for a set of measure zero) buy at everyproduct launch.

The theorem above states that the launch cycle withthreshold z⇤ is implementable in an MPE and is, infact, the only possible Markovian equilibrium out-come. This is a positive result for the firm since z⇤

is the minimum threshold for the firm, as consumerswould balk at purchasing new products if they wereintroduced any more often. This is driven by the factthat the firm has market power: all consumers areinfinitesimal and no one individual per se affects thefirm’s profit. Along the equilibrium path, the con-sumers choose to purchase at every time when thereis a launch, so the outdatedness profile is alwaysidentically equal to O4t5= 4401155. Consumers, beinginfinitesimal, cannot individually change the outdat-edness profile of the market. Therefore, verifyingwhether a deviation from the equilibrium path is prof-itable does not involve determining what consumerswould do in other states of the game with differentoutdatedness profiles. We highlight that even thoughwe do not determine what happens in many of theoff-the-equilibrium-path states, our theorem appliesin a setting with subgame perfection since the setof MPEs is a subset of the class of subgame per-fect equilibria. Even though the equilibrium path isunique, there is multiplicity of equilibria. There existasymmetric MPEs where a mass of consumers of mea-sure zero does not buy at every launch. There isalso the possibility of multiplicity due to differentactions being taken at off-the-equilibrium-path statesthat cannot be reached via unilateral deviations.In the next section, we explore whether the firm can

do better than release a new product every time thetechnology improvement reaches the threshold z⇤. Inparticular, we explore the optimal launch strategy ofa firm that is able to commit to technology levels offuture launches.

5. Optimizing Launch CyclesWe now consider the case where the firm decideson a launch policy in advance and announces it tothe consumer market. The firm decides the sequenceof technology levels of its products in advance, andthe consumers respond by selecting the products thatoptimize their own utilities. We assume that the firmhas commitment power, so that it is able to makecredible promises about future generations’ technol-ogy levels. In practice, firms do not announce entiresequences of product releases in advance, but theyoften do make announcements about upcoming prod-ucts. The formulation studied in this section, with thefirm being able to commit to an entire path of future

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Lobel et al.: Optimizing Product Launches in the Presence of Strategic ConsumersManagement Science 62(6), pp. 1778–1799, © 2016 INFORMS 1787

launches, models a best-case scenario for the firm andthus allows us to consider what types of announce-ments are valuable for the firm. We show below thatthe firm does not in fact need to be able to commit toentire technology paths in advance in order to imple-ment the optimal policy.In our model, the firm first announces all technology

levels of future product generations. The firm commitsto a launch policy, which is represented by its set oftechnology levels z. In our framework, the firm doesnot make commitments with respect to the future tim-ing of product launches, only technology levels. Theset of policies available to the firm Sf is thus equalto the set of subsets of the positive real numbers 2✓+ .The launch date íi associated with a given launch tech-nology level zi is thus the hitting time of the Brow-nian motion that represents the technology process.The consumers then respond by making purchases asa function of the launch policy and the stochastic tech-nology process. Therefore, a consumer’s strategy setat time t is represented by Sc

t 2 2✓+ ⇥Ït ! 80119, with

t 2  à whenever sàt 4z1ót5= 1. The consumer strategyspace is the collection of strategy sets available to himat all times; i.e., Sc = 8Sc

t 9t .The firm would like to maximize its expected util-

ity subject to the consumers’ optimal response. Thefirm’s product launch optimization problem can thusbe formulated as follows:maximize

z22✓+sà2Sc1 à260117

⇧6Uf 4z1 8sà9à57

s.t. ⇧6Uc4z1 4sà01 8sà9à 6=à055 óót7

� ⇧6Uc4z1 4s̄à01 8sà9à 6=à055 óót7

for all t1 ót 2Ït1 à0 2 601171 s̄à0 2 Sc0

(OPT-1)

In the formulation above, the firm selects its launchpolicy z and its consumers’ purchasing behavior 8sà9à,but it is restricted by a consumer incentive compati-bility constraint. This constraint ensures that no focalconsumer à0 wants to deviate from his strategy sà

0 toa different strategy s̄à

0 at any possible sample path ót

of the technology evolution.The firm and the consumers clearly have conflict-

ing interests regarding a desirable outcome. The firmwould like to release products and have consumersbuy them as frequently as possible. Because of dis-counting, the firm would also like purchases to occurearlier rather than later. Meanwhile, consumers needto accumulate value from each purchase and thereforeprefer to wait until a product release contains enoughtechnological improvement to justify a new expendi-ture. Thus, the firm’s challenge is to find a launchpolicy that leads consumers to buy as often and asearly as possible.The first step in our analysis is to simplify the con-

sumer’s incentive compatibility constraint. Our first

lemma shows that there exists a symmetric equi-librium where consumers buy all products the firmreleases. We introduce a subset of the consumer strat-egy space Sc, to which the consumer can restrict him-self without loss of optimality. These are strategieswhere the consumer buys products if, and only if,they have certain technology levels, and where con-sumers buy these products immediately after they arereleased. With a slight abuse of notation, we say theconsumer is playing strategy q 2 2✓+ if he buys exactlythe set of products released with technology level inthe set q and does so immediately upon each productrelease.

Lemma 2. There exists an optimal solution of OPT-1where all consumers purchase at every time when there isa new product launch; i.e., q= z. In this solution, the con-sumers’ policy q= z constitutes a best response if, and onlyif, ⇧6Uc4z1q57� ⇧6Uc4z1 q̄57 for all q̄ ✓ z. In this solution,z can be represented by a sequence of launch technologylevels 8zi9i2�, where zi < zi+1 for all i 2�.

The consumers have no incentive to buy productsat any point other than launch dates as they cananticipate purchases to their respective release datesand thus use more advanced products earlier and forlonger periods of time. Meanwhile, if a firm intro-duces a product that the consumers do not buy, thefirm can improve on its policy by removing this par-ticular product launch. The lemma allows us to sim-plify OPT-1 to a search over a single sequence z:

maxz22✓+

⇧6Uf 4z1z57

s.t. ⇧6Uc4z1z57� ⇧6Uc4z1 q̄57 (OPT-2)

for all q̄✓ z0

The constraints in the formulation above are stillunwieldy since they require the consumers to comparetheir set of purchase technologies z with any possiblealternative set of purchase technologies q̄✓ z. The nextlemma and the subsequent proposition allow us to sig-nificantly simplify the consumer’s problem.

Lemma 3. For any given z = 8zi9i2�, the function⇧6Uc4z1q57 is submodular in q when restricted to thedomain of subsets of z.

The lemma above shows that the expected utility ofthe consumers is submodular in their purchases. Thatis, for two given consumer policies q0 ⇢ q00 ⇢ z, addingan extra purchase of technology q̂ 2 z\q00 adds morevalue to policy q0 than to policy q00. In other words,from a consumer’s perspective, multiple generationsof the firm’s product constitute a set of imperfectlysubstitutable goods: early generations of the productcreate value by being available early, whereas late gen-erations create value by containing advanced technol-ogy. Thus, the more products a consumer purchases,

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Lobel et al.: Optimizing Product Launches in the Presence of Strategic Consumers1788 Management Science 62(6), pp. 1778–1799, © 2016 INFORMS

the less value he obtains from adding a new pur-chase. Note that, though the function ⇧6Uc4z1q57 issubmodular in q for any given z, it does not followthat ⇧6Uc4z1q57 is a monotone function of q. In fact,adding additional purchases to a set q can certainlyhave a negative impact on the consumer’s overall util-ity. The following proposition leverages this submod-ularity result to show that the consumers can considerone product at a time when deciding whether to makepurchases.

Proposition 1. For a firm’s launch policy z, the con-sumer’s purchasing policy q= z is a best response if, andonly if, ⇧6Uc4z1z57� ⇧6Uc4z1z\8zi957 for all i 2�.

This proposition is one of the key simplifying ideasthat makes the launch policy optimization problemtractable. Instead of considering whether a large groupof purchases are collectively worth their price, a con-sumer need only think if each one of them is indi-vidually worth it. Its proof relies on the submodular-ity established in Lemma 3: an additional purchase ziadds less value to the set of purchases z\8zi9 thanto any other smaller set of purchases q̄ ⇢ z\8zi9. Thisproposition is particularly useful because the net util-ity from excluding purchase zi from the consumer pol-icy z depends only on the technologies ziÉ1, zi, andzi+1, as given by

⇧6Uc4z1z57É ⇧6Uc4z1z\8zi957= ⇧

eÉÑíi

4zi É ziÉ15v

Ñ41É eÉÑ4íi+1Éíi55É p

��0 (5)

The only relevant pieces of information from the setof launch technologies z for deciding whether pur-chasing the product with technology zi is worth it forthe consumer are ziÉ1, zi, and zi+1. Proposition 1, com-bined with Equation (5), has the following importantimplication.

Observation 1. The firm can implement anylaunch policy z = 8zi9i2� by committing to the tech-nology level zi+1 whenever it releases a new productof technology level zi.

That is, there is no need for the firm to commit to itsentire launch sequence at time t = 0. Instead, the firmcan implement its launch policy by simply announc-ing the technology level of the following launch everytime it introduces a product. In fact, we argue belowthat the firm does not even need to commit to a tech-nology level after every launch in order to implementthe optimal policy.The formula in the right-hand side (RHS) of Equa-

tion (5) can be simplified. To determine whether itis nonnegative, we can ignore the always positiveterm eÉÑíi . Furthermore, ⇧6eÉÑ4íi+1Éíi57 is the moment-generating function of the hitting time of zi+1Ézi by a

Brownian motion with drift å and variance ë2. In theproof of Lemma 1, we use a result from Karatzas andShreve (1991) to argue that ⇧6eÉÑ4íi+1Éíi57 = eÉ„4zi+1Ézi5,where „ is defined in Equation (4). We can furthersimplify the formula by writing it in terms of the dif-ference in the technology levels, rather than the levelsthemselves. With a change of variables to r1 = z1 andri = zi É ziÉ1 for all i � 2, Equation (5) is nonnegativeif, and only if,

riv

Ñ41É eÉ„ri+15É p� 00

We can also simplify the firm’s utility functionunder a firm policy z and a consumer policy z to

Uf 4z1z5= 4pÉcÉK5àX

i=1

⇧6eÉÑíi 7= 4pÉcÉK5àX

i=1

eÉÑPi

j=1 rj 1

where the second equality combines the fact thatzi =

Pij=1 rj with the same moment-generating func-

tion argument from the proof of Lemma 1. Theterm pÉ cÉK is a positive constant and can thus beignored. With the two equations above, we can recastthe firm’s launch optimization problem as the follow-ing deterministic problem:

maxri2601à71 i2�

àX

i=1

eɄPi

j=1 rj

s.t. ri41É eÉ„ri+15� Ñp

vfor all i 2�0

(OPT-3)

In the formulation above, we explicitly allow the deci-sion variables to take value infinity, which will occurif the optimal policy contains only finitely many prod-uct launches.The next theorem establishes the optimal solution

of the firm’s launch policy optimization problem andis one of our main results. It involves a launch pol-icy that we denote as the 2-cycle, where the firmintroduces new generations of its product accordingto interlaunch technology levels 4r11 r21 r11 r21 0 0 0 1 5 forsome values r1 and r2.

Theorem 2. The unique optimal launch policy is thefollowing:• If v/4p„Ñ5 1/ã, then the firm should launch a sin-

gle generation of the product with technology level 4Ñp5/vand subsequently exit the market.• If v/4p„Ñ5 > 1/ã, then the firm should launch new

product generations in accordance with a 2-cycle policy withcycles r1 < r2, where r1 is the unique solution of the equation

pÑ4eÉ„t + 1+„t5= 2v„t21 (6)

and r2 = 41/„5 log4vr1/4vr1 É p„55,whereã is the unique solution of the equation 4ãÉ 15eã = 1.1

1 We can write ã in terms of the Lambert W function as ã =W 41/e5+ 1, which yields ã ⇡ 1027846. The Lambert W function isdefined implicitly by the equality z=W 4z5eW 4z5 for all z.

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Lobel et al.: Optimizing Product Launches in the Presence of Strategic ConsumersManagement Science 62(6), pp. 1778–1799, © 2016 INFORMS 1789

Figure 3 (Color online) Values of r1 and r2 as Determined byTheorem 2

0 0.2 0.4 0.6 0.78 1.0 1.2 1.4 1.6 1.8 2.00

2

4

6

8

10

12

14

Consumer valuation v

Tec

hnol

ogy

gaps

r1

and

r 2 r1r2

Notes. The parameters p, Ñ, and „ are kept constant at 1. The value v =00782 is the threshold between the single launch and the 2-cycle regimes.

To prove this theorem, we relax OPT-3 by remov-ing all the constraints associated with even valuesof i. This relaxed problem can be solved explicitlybecause all remaining constraints (i= 113151 0 0 0) mustbe binding as the objective function is decreasing inall ri’s, the constraints are increasing in all ri’s, andeach variable ri appears in exactly one constraint.Note that there are two ways in which the constraint

r141É eÉ„r25= Ñp

v

can be true: either r1 = Ñp/v and r2 =à or r1 > Ñp/vand r2 <à. This gives rise to the two possible opti-mal regimes. The solution of the relaxed problem iscompleted by a decoupling argument, which showsby symmetry that all odd ri’s take the same value(thus, all even ri’s also take the same value). The finalstep of the proof is to verify that the solution of therelaxed problem is feasible in OPT-3 and, therefore, isan optimal solution of this problem as well.The technology gaps of the optimal launch policy

are depicted in Figure 3. The theorem shows that thekey ratio for determining the optimal launch policyis v/4p„Ñ5, which can be interpreted as the product’slong-term technological value, with the understandingthat a low value means that the consumer expendi-ture is amortized slowly over time. For instance, thisoccurs when v/p is low, and the product gains lit-tle value over time compared with its relatively highprice. Low drift å and low variance ë2 also lead tolow long-term technological value through high „. Itmight seem counterintuitive that low drift has a sim-ilar effect to low variance, but both lead to new prod-ucts being introduced less often. This phenomenon issimilar to what occurs with financial options, whereboth higher expected returns and higher variance leadto higher option prices. This occurs because releas-ing a new product is an option for the firm, one thatit will not choose to exercise unless the technology

level goes up from the previous release. Beyond that,if the future is heavily discounted (Ñ is high), thenthe product is of low long-term technological valuesince the next time when consumers would purchasean upgrade of the product will occur at a time thatis so far into the future that the net present value ofthis eventual upgrade is small. In this scenario, theoptimal policy for the firm is to introduce the prod-uct once and stop its development immediately after.That is, for a product of low long-term technologicalvalue, the firm is better off discontinuing the prod-uct than producing successive generations of it. Notethat this occurs even though our model assumes thefirm’s technology evolves exogenously, and therefore,the firm does not save any sort of research expendi-ture by discontinuing a product. This occurs solelybecause the firm can bring forward in time the con-sumers’ (first and only) purchase by committing tonot releasing upgrades. If no upgrades will ever beavailable, the consumers will expect a higher surplusfrom the purchase and thus be willing to buy it ear-lier, thus benefiting the firm, though overall its totalprofits will be on the low side.By contrast, the firm’s optimal policy is to introduce

a series of upgrades over time if the product has ahigh long-term technology value v/4p„Ñ5. In this case,the firm’s optimal launch policy is a 2-cycle one wherea major technology improvement follows a minor one.Recall from §4 that when the firm does not announcea launch policy, it ends up in an equilibrium whereit introduces products according to a 1-cycle policy.By committing to future launch dates, the firm canimprove its profits by shortening the length of half ofits launches (i.e., by launching a product with a minortechnology improvement with respect to the previousrelease). In fact, as a practical matter, the firm onlyneeds to precommit to the major cycle, whereas theminor cycle could be executed on the go. Further-more, it only needs to commit not to launch a newproduct too early. That is, at the moment of releasinga new product on the go (i.e., ending a minor cycle),the firm announces that the next launch will not occuruntil a given date or until a certain technological levelis achieved. This announcement will trigger earlypurchases from the consumers that otherwise wouldchoose to wait. Once the major cycle is completed, thefirm does not need to make any announcements butcan instead release the next product as an on-the-golaunch. Note that our analysis does not recommendin any way that the firm withhold technology from alaunch or that it launch substandard products. Underthe optimal policy, the firm always releases the besttechnology it currently has available and the firm onlyreleases products the consumers will find desirable,because all products launched satisfy consumer incen-tive compatibility constraints.

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Lobel et al.: Optimizing Product Launches in the Presence of Strategic Consumers1790 Management Science 62(6), pp. 1778–1799, © 2016 INFORMS

The magnitude of v/4p„Ñ5 defines the shape of thetwo cycles. When the long-term technological valuev/4p„Ñ5 is high, the firm will release products often.In this case, attempting to anticipate the first customerpurchase by delaying the second release date is not aparticularly valuable tactic for the firm, and r1 will beonly slightly smaller than r2. In the limit as v/4p„Ñ5goes to infinity, r1 is equal to r2, and it turns out thatpreannouncing product launches converges to the on-the-go launch policy z⇤ characterized in Theorem 1, sothat r1 = r2 = z⇤ (see the proof of Theorem 2). On theother hand, if v/4p„Ñ5 is only slightly above 1/ã, thetwo cycles will be very asymmetric. As the long-termtechnological value approaches 1/ã from above, thesecond cycle r2 becomes increasingly large, eventuallyconverging to the single launch solution.

6. Price OptimizationOur analysis has assumed so far that the price in bothscenarios (launching products on the go and at pre-announced times) is exogenously given. The optimalpolicy in each case is defined by cycles whose defini-tion depends on a given price p. In this section, weextend the analysis to a situation where the price isendogenously determined. Namely, we characterizethe optimal joint pricing and product launch policyfor both scenarios. In both cases, we assume that asingle price p is chosen by the firm at t = 0 and thatthe firm uses this price throughout the game.

6.1. Optimal Pricing for Launching ProductsOn the Go

In §4, we considered the firm’s launch policy in theMarkov perfect equilibrium that occurs when the firmlaunches products on the go and showed, in Theo-rem 1, that the equilibrium path is given by a singlecycle z⇤, where z=  à = 8z⇤12z⇤13z⇤1 0 0 09 for all à. Thefirm’s expected utility function (see Equation (2)) isthus given by

⇧6Uf 4z1z57 =àX

i=1

44pÉ cÉK5eÉ„iz⇤5

= 4pÉ cÉK5eÉ„z⇤

1É eÉ„z⇤ 0 (7)

Recall from Lemma 1 that, for a given price p, theoptimal cycle length z⇤ is the unique solution to Equa-tion (3). Hence, the associated optimal price function pmust verify

p= vz⇤41É eÉ„z⇤5

Ñ0 (8)

Since v, Ñ, and z⇤ are all nonnegative, the RHS of theequation above is increasing in z⇤, and thus, there isa one-to-one correspondence between cycle length z⇤

and associated optimal price p. Substituting Equa-tion (8) into Equation (7), we obtain the firm’s joint

price and cycle length optimization problem just as afunction of z⇤. We denote the firm’s expected utilityby ⇧6Uf 4z1z57; i.e.,

⇧6Uf 4z1z57=✓vz⇤41É eÉ„z⇤5

ÑÉ cÉK

◆eÉ„z⇤

1É eÉ„z⇤ 0 (9)

This function is unimodal in the cycle length z⇤, andgiven the optimality condition of Equation (8), we getthe following.

Proposition 2. For the equilibrium path obtained inTheorem 1, the firm’s expected utility function is unimodalin price.

The optimal price does not have a closed-formexpression, but it can be computed by a simple one-dimensional line search.

6.2. Optimal Pricing forPreannounced Introductions

In §5, we considered the optimal launch policy whenthe firm commits to a preannounced schedule oflaunch technology levels. For a given price p, Theo-rem 2 characterizes the two possible outcomes: eithera single introduction or a 2-cycle sequence of minorand major interlaunch technology levels. When thereis a single introduction, the technology level of thisintroduction r1 is equal to pÑ/v, which is strictlyincreasing in p. Likewise, when there are multipleintroductions, the unique solution r1 to Equation (6)is strictly increasing in p. In either case, there is a one-to-one correspondence between r1 and p. Moreover,in the 2-cycle policy, the long cycle r2 is also uniquelydetermined from r1 (and, therefore, from p).The following theorem characterizes the optimal

price for each of the two possible optimal launchpolicies.

Theorem 3. Let ã be defined as in Theorem 2. Thefirm’s profit function is unimodal in price, conditionallyon the firm utilizing the optimal launch policy for anygiven price. In particular, the optimal price is given by thefollowing:• If v/44c+K5Ñ„5 1/4ãÉ 15, then the single launch

policy is optimal, with price

p⇤ = c+K+ v

Ñ„0 (10)

• If v/44c+K5Ñ„5> 1/4ãÉ15, then the 2-cycle launchpolicy is optimal, with price

p⇤ = 2v„4r⇤1 52eÑr⇤1

Ñ41+ eÑr⇤1 41+ Ñr⇤1 55

1 (11)

where r⇤1 is the unique positive solution to the equation

„34c+K5+ 2„24c+K54eÉ„r1+15r1

+„4c+K54eÉ„r1+152

4r152

+ 2v„41ÉeÉ2„r15

Ñr1É 2„3vr1

Ñ=00 (12)

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Lobel et al.: Optimizing Product Launches in the Presence of Strategic ConsumersManagement Science 62(6), pp. 1778–1799, © 2016 INFORMS 1791

Figure 4 (Color online) Joint Launching and Pricing Policy for the Preannounced Introduction Case

2 8! /" 10 12 14 16 180

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

18,000

20,000

r1

r*1

Firm

’s u

tility

Two-cycle launchSingle launch

0

20,000

40,000

80,000

100,000

120,000

140,000

160,000

180,000

p*

2 4 8! /"

!# /$"

10 12 14 16 18

r1

r*1

p

Notes. Parameter values are v = 21000, c = 0, Ñ= 002, å= 1, ë = 0, and K = 300. Left: firm’s expected utility as a function of r1, assuming that the pricecharged is the unique optimal p4r15. In this case, the optimal minor launch is given by r ⇤1 = 4064. Right: bijection between r1 and p4r15. In this case, the optimalminor launch is given by r ⇤1 and maps onto a unique optimal price p⇤ = p4r ⇤1 5= 371065. The associated major launch cycle is given by r ⇤2 = 8002.

The proof establishes a bijection between r1 andp4r15, and then it rests on the unimodality of thefirm’s utility function in r1. Specifically, for any givenp > c + K, there is a unique corresponding r14p5 thatsolves the firm’s profit optimization problem (OPT-1)or after taking the inverse, there is a well-definedfunction p4r15.Figure 4 illustrates the firm’s utility function for

the joint launching and pricing problem. The graphin the left plots the firm’s utility as a function ofthe minor cycle phase r1 when the price charged isthe unique p4r15. The graph in the right shows thebijection between r1 and p4r15, so that the uniqueoptimal r⇤1 maps onto a unique optimal price p⇤ =p4r⇤1 5. This is given by the linear relation p⇤ = vr⇤1 /Ñin case r⇤1 turns out to be big enough (and the firmimplements a single introduction policy). Otherwise,the optimal p⇤ is given by Equation (11).2Observe that for the single-cycle regime, the opti-

mal price p⇤ in Equation (10) is increasing in the fixedlaunch cost K, in the consumers’ valuation v, and inthe variable cost c, and it is decreasing in the dis-count factor Ñ. The same holds for p⇤ in the two-cycleregime, which can be verified from the following twofacts: the RHS in Equation (11) is increasing in r⇤1—and hence p⇤ is increasing in r⇤1—and the left-handside in Equation (12) is strictly decreasing in r1.In Theorem 3, the expression v/44c + K5Ñ„5 plays

the role of the product’s long-term technologicalvalue. Note that when the price is endogenouslydetermined, the aggregate cost per launch c + K

2 For the ease of exposition, in our plots in Figure 4, we haveextended the domain for r1 so that p4r15 goes below the thresh-old c+K. The strict monotonicity of p4r15 is still preserved in theextended domain, though it could lead to a negative utility as indi-cated in the left panel of Figure 4 for r1 sufficiently close to zero.

replaces p compared with the expression in Theo-rem 2. The aggregate cost per launch, which containsthe production cost c as well as the fixed cost K, doesnot affect the long-term technological value of theproduct when the price is exogenous, since it doesnot affect the consumer base. When the price is set bythe firm, however, the aggregate cost per unit is animportant element in determining the retail price ofthe product and, thus, impacts the long-term techno-logical value of the product. Note also that the cost-based version of the long-term technological valuev/44c+K5Ñ„5 that determines the optimal launch pol-icy in Theorem 3 requires a higher bar of 1/4ã É 15for a two-cycle launch policy to be optimal comparedwith the bar of 1/ã for the price-based long-term tech-nological value from Theorem 2.

6.3. The Value of CommitmentWe now compare the profit the firm obtains from uti-lizing a preannounced policy as opposed to launchingproducts on the go. Recall that the optimal prean-nounced policy only requires the firm to announce thelaunch of technology levels for the upcoming productand only to do so at the end of a minor launch cycle,not to announce the entire path of future launches. Inboth scenarios, we assume the firm utilizes the opti-mal joint pricing and launch policy.Table 1 shows for a given aggregate cost per unit

c + K, consumer value v, and discount factor Ñ theoptimal pricing policy and the associated profit foreach scenario. We can see that the utility differencein favor of the commitment case can be significant,with values reaching 12% in the cases listed there.Thus, we observe that when the firm can commit toan introduction policy, it can recover a significant por-tion of the revenues that were left on the table in case

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Lobel et al.: Optimizing Product Launches in the Presence of Strategic Consumers1792 Management Science 62(6), pp. 1778–1799, © 2016 INFORMS

Table 1 Profit Comparison Between On-the-Go and PreannouncedPolicies Under Optimal Prices

On the go (OTG) Preannounced (Prean)

Profit Profitc+K v Ñ p⇤

OTG (p⇤OTG) p⇤

Prean (p⇤Prean) % Gap

30 400 0020 61395074 31661044 71333063 31809009 40030060 773015 392015 882069 409089 40521000 318022 131076 361053 138096 5046

700 0020 111136088 61420049 121773077 61677067 40010060 11301060 698037 11488077 728033 40291000 511025 241034 582050 253002 4084

200 400 0020 61799080 31566070 71771056 31723003 40380060 11089059 318092 11232058 342062 70431000 572031 79059 600 89025 12015

700 0020 111549052 61324002 131220005 61590013 40210060 11649014 616061 11870041 653055 50991000 799053 176089 900 193052 9040

of on the go. We also observe that the discount fac-tor Ñ appears to be the most important factor in deter-mining the gap in profits. This is consistent with thecost-based long-term technological value being pro-portional to 1/4Ñ„5 while being linear in v/4c+K5.

7. Heterogeneous MarketsIn this section, we extend our analysis to a set-ting with multiple customer classes, where differentclasses are characterized by different valuation levelsfor the product. We look first at the case of prean-nounced launches and then at the on-the-go case. Weprovide both algorithms for computing strategies forthese two settings, as well as numerical insights aboutthe role of effects of different market compositionsand discount rates. For simplicity, we assume in thissection that the technology evolves deterministically4ë = 05. Without loss of generality, we assume thatthe technology drift å is equal to 1, so the technologyevolution reduces to Z4t5= t. Throughout this section,we denote as ‰ the number of consumer classes andà the class of a consumer, not the individual identityof a consumer. We let Nà be the mass of consumers inclass à and let và denote the valuation of class à.

7.1. Preannounced Launches withMultiple Customer Classes

We start our analysis by focusing on the case ofpreannounced launches. We demonstrated in Theo-rem 2 that the long-term technological value of thefirm’s product is the key determinant of the opti-mal launch policy. The long-term technological valuedepends, however, on the customer valuation param-eter v. When the market is composed of multiple cus-tomer classes, with some fraction having a high valuefor the firm’s product and another fraction having alow value, should the firm follow a 2-cycle launch

policy (as is optimal when selling to high value cus-tomers), a single introduction (as is in the optimalpolicy for selling to low value customers), or some-thing altogether different? In a market where multipleconsumer classes coexist, it turns out that the firmlaunches products on a regular basis and cannot lurethe low type consumer to purchase early by commit-ting to a single launch. Since products launched forone consumer class are available for all classes, theproduct launch problem invariably gets coupled andneeds to be solved accounting for the full market com-position. Because of this coupling, the heterogeneousmarket problem is hard to address in continuous time.As an approximation, we present here a finite hori-zon, discrete time version of the same problem.

7.1.1. Integer Programming Formulation. All con-sumers are still assumed to value the product in pro-portion to its technology level, but we now allow fordifferent customer classes to have different parame-ters và scaling the value they obtain from the product.The time horizon is finite and discrete, with time slotst = 0111 0 0 0 1T , where T is some large positive integer.We let the consumers and the firm have different dis-count factors: Ñc and Ñf , respectively. We introduce theterms Éc = eÉÑc and Éf = eÉÑf , which are more naturalrepresentations of the discount factors in a discretizedsetting, where a smaller value of É corresponds to amore impatient player.We now argue that the equilibrium of the game

played between the firm and the consumers can becomputed via a single mixed-integer linear program(MIP). We first consider the second stage of the game.That is, we analyze the purchasing problem of a con-sumer of type à for a given sequence of productlaunches. Let xà4t5 be the indicator of the decision topurchase the product at time t. The first problem weformulate establishes a consumer’s optimal purchas-ing policy 8xà4t52 t = 0111 0 0 0 1T 9 for a given launchpolicy 8y4t52 t = 0111 0 0 0 1T 9, where y4t5 2 80119 repre-sents whether a launch occurs at time t:

maximizexà4 · 51wà4 · 1 · 5

TX

t=0

Étc

✓Épxà4t5+ và

tX

t0=1

t0wà4t1 t05◆

subject to wà4t1 t05 xà4t

05 y4t05

for t = 01 0 0 0 1T and t0 = 01 0 0 0 1 t1

4P15 wà4t1 t051 xà4t5 2 80119

for t = 01 0 0 0 1T 1 and t0 = 01 0 0 0 1 t1tX

t0=0

wà4t1 t05= 1 for t = 01 0 0 0 1T 0

In the formulation above, wà4t1 t05, with t0 t, is an

indicator of whether a consumer of type à uses tech-nology t0 at time t. The first inequality in the first con-straint ensures that a consumer of type à who uses

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Lobel et al.: Optimizing Product Launches in the Presence of Strategic ConsumersManagement Science 62(6), pp. 1778–1799, © 2016 INFORMS 1793

technology t0 at time t indeed purchased that technol-ogy at time t0. The second inequality in that constraintprohibits the consumer from purchasing in period t0

if a launch did not occur in that period. Thougha consumer could potentially purchase a product ata period other than its launch date, that is always asuboptimal consumer policy. For any time t0 where thefirm does not launch a product (i.e., y4t05= 0), no con-sumer will own the respective technology level; that is,xà4t

05= 0 andwà4t1 t05= 0 for all t � t0. The last equality

ensures that the consumer owns a technology productat any time t. To meet this constraint before the firstpurchase actually occurs, we impose the ad hoc con-dition xà405= y405= 1. This anchoring is without lossof optimality since it only shifts the consumers’ andfirm’s utility functions by constants (Ép for the con-sumers and pÉ c É K for the firm), which are addedback when reporting results in the next subsection.Problem 4P15 can be seen as a single-dimensional,

uncapacitated facility location with unimodal profits.To cast this as a facility location problem, assumethere is a customer in each location from 1 up to Tand assume that all periods where y4t5= 1 correspondto the possibility of opening a facility at location t.The values of xà4t5 then represent whether a facilityis built on location t, and the values of wà4t1 t

05 rep-resent whether location t0 serves a customer in loca-tion t. This problem has unimodal profit since thebenefit obtained from utilizing facility t0 to serve cus-tomer t is increasing in wà4t1 t

05 for a fixed t (in thisproblem, a facility can only serve a customer if t0 t).This problem is known to have no integrality gap (seeGoemans and Skutella 2004 or Kolen and Tamir 1990),and thus we can instead consider the following relax-ation without loss of optimality:

maximizexà4 · 51wà4 · 1 · 5

TX

t=0

Étc

✓Épxà4t5+ và

tX

t0=1

t0wà4t1 t05◆

subject to wà4t1 t05 xà4t

05 y4t05

for t = 01 0 0 0 1T and t0 = 01 0 0 0 1 t1

4P25 0wà4t1 t051 xà4t5 1

for t = 01 0 0 0 1T and t0 = 01 0 0 0 1 t1tX

t0=0

wà4t1 t05= 1 for t = 01 0 0 0 1T 0

We can simplify 4P25 by removing unnecessaryconstraints. The constraints 0 xà4t

05 1 are redun-dant since 0 wà4t1 t

05 xà4t05 y4t05 1. The con-

straintPt

t0=1wà4t1 t05 = 1 together with wà4t1 t

05 � 0also implies that wà4t1 t

05 1, making this constraintredundant as well. We now utilize the big-M method

to move the constraint xà4t05 y4t5 to the objective

function, obtaining

maximizexà4 · 51wà4 · 1 · 5

TX

t=1

Étc

✓4My4t5É pÉM5xà4t5

+ và

tX

t0=1

t0wà4t1 t05◆

subject to wà4t1 t05É xà4t

05 0

for t = 01 0 0 0 1T and t0 = 01 0 0 0 1 t1

4P35 wà4t1 t05� 0

for t = 01 0 0 0 1T and t0 = 01 0 0 0 1 t1tX

t0=1

wà4t1 t05= 1 for t = 01 0 0 0 1T 0

We now consider the dual of problem 4P35. Letdà4t1 t

05 and cà4t5 be the dual variables associated withthe inequality and equality constraints, respectively.The dual is given by

minimizecà4 · 51dà4 · 1 · 5

TX

t=1

cà4t5

subject to cà4t5+ dà4t1 t05� Ét

cvàt0

for t = 01 0 0 0 1T and t0 = 01 0 0 0 1 t1

4D5 dà4t1 t05� 0 for t = 01 0 0 0 1T 1

TX

r=t

dà4r1 t5= Étc4M + pÉMy4t55

for t = 01 0 0 0 1T 0

We can now formulate the firm’s profit maximiza-tion problem, accounting for the consumers’ bestresponses, as a single MIP. The firm chooses a launchpolicy 8y4t52 0 t T 91 subject to a constraint thatall consumer types respond optimally. We can enforcethe optimality of the consumer response by includingboth the primal and dual variables and constraintsinto the firm’s problem and by adding a new con-straint that ensures that a given type à’s objective isidentical in the primal and dual problems. The MIPthat finds the optimal firm’s policy is given by

maximizey1x1w1 c1d

TX

t=0

Étf

✓ÉKy4t5+ 4pÉ c5

‰X

à=1

Nàxà4t5

subject to y4t5 2 80119 for t = 01 0 0 0 1T 1

wà4t1 t05� 0 for t = 01 0 0 0 1T and

t0 = 01 0 0 0 1 t1

xà4t5 y4t5 for à= 11 0 0 0 1‰ and

t = 01 0 0 0 1T 1

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Lobel et al.: Optimizing Product Launches in the Presence of Strategic Consumers1794 Management Science 62(6), pp. 1778–1799, © 2016 INFORMS

wà4t1 t05 xà4t

05 for à= 11 0 0 0 1‰1

t = 01 0 0 0 1T 1 t0 = 01 0 0 0 1 t1

4F 5tX

t0=1

wà4t1 t05= 1 for à= 11 0 0 0 1‰ and

t = 01 0 0 0 1T 1TX

t=1

Étc

✓Épxà4t5+ và

tX

t0=1

t0wà4t1 t05◆=

TX

t=1

cà4t5

for à= 11 0 0 0 1‰1

cà4t5+ dà4t1 t05� Ét

cvàt0 for à= 11 0 0 0 1‰1

t = 01 0 0 0 1T 1 t0 = 01 0 0 0 1 t1TX

r=t

dà4r1 t5= Étc6M41É y4t55+ p7

for à= 11 0 0 0 1‰ and t = 01 0 0 0 1T 1

dà4t1 t05� 0 for à= 11 0 0 0 1‰1

t = 01 0 0 0 1T 1 t0 = 01 0 0 0 1 t0

In summary, by using a duality argument, we canshow that the seemingly difficult problem of design-ing an optimal launch policy under equilibrium con-straints can be formulated as a single MIP. Once wesolve this problem, to undo the anchoring assumptionthat xà405= y405= 1, we add KÉ 4pÉ c5

P‰à=1Nà to the

optimal objective function value in 4F 5.

7.1.2. Numerical Experiments. In this subsection,we utilize the MIP formulation above and solve thefirm’s utility maximization problem using IBM ILOGCPLEX Optimization Studio V12.4. We test severalmarket effects on the profit performance of the firmand report our findings below.Effect of multiple consumer classes: Our first exper-

iment is aimed at understanding the effect thata multiple-class market has on the firm’s optimallaunch policy. Table 2 compares single-class markets,analogous to the ones studied in §5, to two-classmarkets (i.e., where ‰ = 2). We assume a horizonof length T = 35, which is long enough to avoidend effects given the high discount rate considered

Table 2 Comparison of the Firm’s Launch Policy and Consumers’ Purchasing Times in Homogeneous and Heterogeneous Markets

Firm’s parameter Consumers’ parameters Introduction and purchasing times

K ‰ và Type 1 Type 2 Firm’s profit

0 1 2,000 216181121 0 0 0 132 — 1212291 5,000 — 11415181 0 0 0 132133 2014772 (21000351000) Every three periods 21316181 0 0 0 132133 291641

9,000 1 2,000 216181121 0 0 0 132 — 112221 5,000 — 11415181 0 0 0 132133 210472 4210003510005 216181121 0 0 0 132 216181121 0 0 0 132 131441

Notes. Discount rates are Éc = Éf = 008, price p= 101000, unit cost c= 0, T = 35, and Nà = 1. Type 1 consumers have valuation v1 = 21000, and type 2 havevaluation v2 = 51000.

(Éf = Éc = 008). The product variable cost is set atc= 0.Note that for the single-class markets, the opti-

mal launching policy of this discrete time, finitehorizon approximation mimics the characterizationof the optimal policy for the continuous time, infi-nite horizon case. For instance, in the first row inTable 2, consumers in a homogeneous, low-valuemarket alternate between cycles of lengths 2 and 4(i.e., a minor launch is followed by a major launch).Under this policy, the firm can induce low valueconsumers to purchase as early as in period 2 bypushing the next launch to period 6. Similarly, ina homogeneous high-value market, consumers alter-nate cycles of lengths 1 and 3 (see the second row inTable 2), though now, since consumers’ valuation ishigher (and therefore, the long-term technology valuev/4p„Ñc5 is higher), the seller is able to introduceproducts more frequently.When both consumer classes coexist in the market,

they become coupled, completely altering the productintroduction and purchasing patterns, even if there isno fixed cost for launching a product. The third rowin Table 2 reports the purchasing times of both classeswhen coexisting in the market. The effective productintroduction times are the union of these two sets ofpurchase times, which is different from the union ofthe launch times of the two separate markets. Recallfrom §5 that the rationale behind the 2-cycle pol-icy is to trigger earlier purchases from strategic con-sumers who would otherwise wait. However, whenthe firm faces such distinct segments, it has to intro-duce products less often compared with the unionof both purchasing patterns in isolation (e.g., it doesnot introduce at t = 4). Since the firm cannot targetjust one of the segments, it has to compromise thewillingness to buy of both classes. For a group ofcustomers with a given valuation, the addition of asecond cohort with a different valuation can be ben-eficial, because it restricts the firm’s ability to use anoptimal launch policy directed at extracting more rev-enue from that particular customer class. In Table 2,the low value customers are thwarted from buying

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Lobel et al.: Optimizing Product Launches in the Presence of Strategic ConsumersManagement Science 62(6), pp. 1778–1799, © 2016 INFORMS 1795

Table 3 Effect of Different Degrees of Consumers’ Heterogeneity

Consumers’ parameters Introduction and purchasing times

‰ Nà v Õ= 4và5 Type 1 Type 2 Type 3 Firm’s profit

1 3 12,000 3171 0 0 0 131 Same as type 1 Same as type 1 245,4513 1 (10100031210003141000) 3181141 0 0 0 131 3171 0 0 0 131 Same as type-2 231,2463 1 481000312100031610005 61101 0 0 0 132 3171 0 0 0 121126132 3171 0 0 0 120123126132 201,6993 1 461000312100031810005 Every six periods 3, 7, 11, 15, 18, 22, 25, 29, 34 Every three periods 203,5523 1 441000312100032010005 7, 15, 23, 29 5, 10, 15, 18, 22, 26, 29 2151 0 0 0 126129133 194,6723 1 421000312100032210005 13, 26 Every four periods 2151 0 0 0 132134 188,487

Note. Parameters are T = 35, c= 0, K = 11000, p= 901000, and Éf = Éc = 008.

every three periods when they are the only customersaround (first row), but they are able to do so whenthey coexist with high value customers (third row).Overall, the total profit the firm obtains when bothclasses of customers are present together is 9% lessthan the sum of the profits it would obtain when fac-ing two separate single-class markets.The product launch cost also plays an important

role in the firm’s launch policy. For instance, whencomparing the scenario without launch costs vis-à-vis the one where K = 91000, we see that in the for-mer, there are time epochs when just one consumerclass makes a purchase (e.g., at t = 2 and t = 8, onlythe high value consumers buy when K = 0; see thethird row in Table 2). Since the product launch costis smaller than the revenue from any single consumerclass, the firm may choose to introduce at time epochsin which only one consumer class will purchase theproduct. However, when K = 91000 and p = 101000,the profit of 11000 from selling to a single class of cus-tomers is far below the profit of 2⇥ 101000É 91000=111000 from selling to both classes, thus leading thefirm to only introduce at times when both segments ofthe market buy together, as indicated by the purchasetimes of both classes in the last row in Table 2. In suchsituations, the firm launches products according tothe optimal policy for selling to low value customerssince the high value class who prefers more frequentintroductions will always buy. With high fixed costs,the firm benefits from the presence of multiple con-sumer classes since the firm can pool classes to reducethe impact of the fixed launch costs.Effect of consumer’s heterogeneity: Table 3 illustrates

the effect of different degrees of market heterogeneityon the consumers’ purchasing behavior and on theoptimal introduction policy. The consumer valuationv= 121000 is set as the reference point (first row), andfrom there onward, different ranges of dispersion ofthe valuations are evaluated. The market size is thesame for all cases, but its composition varies. Whenthere are three different types present in the market,each type accounts for a third of the total market size.

Because the market composition of the consumershas wider spread in terms of valuations, it is diffi-cult for the firm to target any single consumer classto extract surplus. Since the consumers with low val-uation would like to purchase new versions of theproduct less often compared with the consumers withhigh valuation, it is very likely that, when there arehigh valuation consumers present in the market, theoptimal launch policy for the firm is characterized byfrequent launches. Low valuation consumers wouldfree ride over high valuation ones, taking advantageof these frequent launch times to pick their purchas-ing times and skip some of the launches so as to retainmuch of their surplus. This is verified, for instance,when comparing the frequent purchases of low valu-ation type 1 consumers who purchase with cycles oflengths 3 and 4 in the first row in Table 3 but spacetheir purchases as the market becomes more hetero-geneous, with a cycle of length 13 in the last row.Hence, the firm is incapable of extracting as muchsurplus from the low valuation consumers, as in thecase when it tailors the product launch dates target-ing only such consumers. We can see this effect in thedecreasing profits of the firm from Table 3 as the val-uations of the different consumer classes get fartherapart.3Effect of discount factors: For a single-class market,

we study the effect of varying the consumers’ dis-count rate. The results are reported in Table 4, andthey verify what was sketched in Figure 3. Here, thenumber of periods in the horizon is set at T = 45. AsÉc decreases (i.e., as Ñc increases, consumers becomemore impatient), we observe a shift in the launch pol-icy regime from multiple launches for Éc = 008 andÉc = 007, to a single launch for Éc 006.4 Since the

3 Note that the values in the third and fourth rows are inverted withrespect to a decreasing order of profits, which is due to end effectsof the finite horizon formulation of the problem. Nevertheless, thedifference between both values is only of the order of 1%.4 The consecutive introduction times toward the end of the horizonfor Éc 006 are due to the deep discount rates that translate intoextremely low long-term technology values for the consumers, con-tributing to the solution within the margin of error of the CPLEXsolver.

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Table 4 Consumers’ Patience and Launch Policy

Consumers’ discount Introduction and purchasing Firm’sfactor Éc times profit

0.80 6, 15, 21, 30, 36 6,1620.70 8, 16, 24, 32, 42 4,0300.60 10, 41–45 2,1540.56 11, 37–45 1,7400.52 12, 37–45 1,3960.48 13, 34–45 1,146

Note. Parameters are T = 45, K = 301000, p = 501000, Éf = 008, c = 0,‰= 1, Nà = 1, and v = 21000.

Table 5 Effect of Firm’s and Consumers’ Patience

Introduction and purchasing timesFirm’s Consumers’discount discount Firm’sfactor Éf factor Éc Type 1 Type 2 profit

0.5 Every 4 periods 11415181 0 0 0 132134 616060.7

8<

: 0.8 Every 3 periods 2131618191121 0 0 0 132133 151886Every 3 periods 2131618191121 0 0 0 132133 291449

0.8

)

0.7 Every 3 periods 2131618191121 0 0 0 132133 2914490.5 Every 4 periods Every 2 periods, 33, 35 241549

Note. Parameters are K = 100, p= 101000, ‰= 2, N1 = N2 = 1, c = 0, andv = 4210003510005.

consumers would buy less often to overcome the pur-chase cost and gain utility through use of the product,the firm would prefer to induce a single early pur-chase from the consumers compared with very sparsepurchases later in the horizon.In Table 5, in a heterogeneous market with two con-

sumer classes, we vary the values of Éf = exp4ÉÑf 5and Éc = exp4ÉÑc5 (all else being equal) to illustratethe effect of the firm’s and consumers’ discount fac-tors on the launching and purchasing policies. Weassume a horizon of length T = 35.For a given degree of consumers’ patience Éc,

when the firm is more impatient than the consumers(i.e., Éf < Éc), its profits grow as the discount factorapproaches Éc. On the other hand, in the more realis-tic setting where consumers are more impatient than

Table 6 Value of Market Information

Consumers’ parameters Actual purchasing times Firm’s outcome

‰ Nà và Type 1 Type 2 Launches Realized profit Profit under complete info

1 2 12,000 3171 0 0 0 131 3171 0 0 0 131 3171 0 0 0 131 1631330 163,3302 1 410100031410005 7, 14, 21, 28, 31 3171 0 0 0 131 3171 0 0 0 131 1051126 152,9602 1 48100031610005 7, 14, 21, 28 3171 0 0 0 131 3171 0 0 0 131 1051037 140,6762 1 46100031810005 7, 14, 21, 28 3171 0 0 0 131 3171 0 0 0 131 1051037 141,1322 1 44100032010005 7, 14, 21, 28 3171 0 0 0 131 3171 0 0 0 131 1051037 150,8272 1 42100032210005 14, 28 3171 0 0 0 131 3171 0 0 0 131 851333 134,535

Note. Parameters are T = 35, c= 0, K = 11000, p= 901000, and Éf = Éc = 008.

the firm, and moreover, when they become increas-ingly impatient (i.e., Éc decreases), their utility froma given purchase decreases. This affects both con-sumer types in different ways: the low type 1 mustuse the product for a longer time to recover enoughutility from it—this is observable in the longer inter-purchasing cycles in the last row of Table 5—whereasthe high type 2 will buy more regularly. Overall, thefirm’s profits go down as consumers become moreimpatient.Value of market information: Table 6 shows the value

of precise market information for the firm in terms ofconsumer valuations. Suppose that the firm believesthat the consumers are homogeneous with a cer-tain valuation, and it launches products assuming so,whereas in reality the market composition is different.In this case, the consumers’ purchasing time epochsmay be different from what the firm would expect. InTable 6, the total population mass is set at 2. Through-out, the firm assumes that the market is homogeneouswith valuation v = 121000. The “Consumers’ param-eters” column shows the true valuation mix definingthe market composition, with Nà = 1 for the second tosixth data row.We observe that misinformation regarding the con-

sumer valuations can severely hurt the firm. To illus-trate, from the last row, we observe that a broadspread between the firm’s belief and the actual val-uations lowers the firm’s profits by 58%. That is, thefirm would have gained an additional profit of 49,202if it knew that the true valuation mix of the market is42100032210005 rather than misestimating consumersas being homogeneous at v= 121000.

7.2. Launches On the Go withMultiple Customer Classes

We now turn our attention to on-the-go launch poli-cies when there are consumers with different valua-tions in the market. Like we did for preannouncedlaunches, we first propose an algorithm for findingequilibria and then proceed to provide some numeri-cal insights.

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7.2.1. A Backward Induction Approach. In thissubsection, we propose a method for computing equi-libria for the on-the-go launch case. As we did forthe case of preannounced launches, we replace ourcontinuous time, infinite horizon model with a dis-crete time, finite horizon version.Let ‰ be the number of consumer classes, with

Nà being the mass of consumers with valuation và

for any à 2 81121 0 0 0 1‰9. The methodology we offerapplies to any finite number of consumer classes, butthe computational burden does grow exponentially inthe number of classes. Our method involves solvingfor the subgame perfect equilibrium of a slightly dif-ferent game than the one we studied before, wherewe replace each consumer class by a single represen-tative consumer. Each consumer class à is replaced bya representative consumer who makes purchases at aprice pNà, at a cost to the firm of cNà. The equilibriumof this game between representative consumers is notnecessarily the same as the equilibrium of the originalgame with infinitesimal consumers. However, it doesprovide a candidate equilibrium path. We can testwhether any infinitesimal consumer would want todeviate from the equilibrium of this game. Note thatthe deviation is different here, because an infinites-imal consumer deviating does not change anyoneelse’s utility except his own. Fortunately, this method-ology worked in our numerical experiments, by gen-erating an equilibrium for the game with infinitesimalconsumers in over 90% of instances tried. We do notknow whether symmetric equilibria—where all con-sumers belonging to the same class make identicaldecisions—exist in the instances where this methodfails.The main advantage of replacing the consumer

classes by representative consumers is that we reducethe state space of the problem to a finite set. Forevery period t 2 80111 0 0 0 1T 9, the set of possible statesare represented by the technology available in themarket w4t5 and the technologies owned by the dif-ferent consumers Cà4t5. We solve this problem bythe standard technique for finite horizon dynamic

Table 7 Comparison of the Firm’s Launch Policy and Consumers’ Purchasing Times in Homogeneous and Heterogeneous Markets

Firm’s parameter Consumers’ parameters Introduction and purchasing times

K ‰ Nà và Type 1 Type 2 Firm’s profit

0 1 1 2,000 316191 0 0 0 127132135 — 1014831 1 5,000 — Every two periods, 35 1717762 1 4210003510005 Every three periods, 35 Every two periods, 35 281259

9,000 1 1 2,000 316191 0 0 0 127132135 — 110481 1 5,000 — Every two periods, 35 117772 1 4210003510005 316191 0 0 0 127131135 316191 0 0 0 127129131133135 111534

Notes. Discount rates are Éc = Éf = 008, price p= 101000, unit cost c= 0, and T = 35. Type 1 consumers have valuation v1 = 21000, and type 2 have valuationv2 = 51000.

games: backward induction. We expand the set ofperiods to twice their original horizon, to accountfor the fact that in each period the firm first chooseswhether to release a new product, with consumerssubsequently deciding whether or not to buy. Call theperiods where the firm acts tf and the periods wherethe consumers act tc. We start from the last period,T c, and consider for every possible state whether eachparticular representative consumer buys the productat that state. Once the values of those states are cal-culated, we take a step back to period T f . For eachpossible state at time T f , we calculate whether thefirm launches given the continuation value of thatstate. We then naturally proceed to state 4T É 15c,where the consumers play a bimatrix game to decidewhether to buy the product at each possible state.We repeat these steps inductively all the way backto time 0f , where the firm will obviously not launcha product with zero technology. By following thestates chosen by the firm and the consumers start-ing from time 0f , we find the equilibrium path ofthe game.

7.2.2. Numerical Experiments. We now present afew numerical results for the multiple-consumer classmarket when the firm announces products on the go.We note the effects found here mostly replicate thecase of preannouncing.Effect of multiple consumer classes: As with prean-

nouncing, having multiple consumer classes can leadto coupling of purchasing behavior, since a productrelease for one class is also available for the other.However, our numerical experiments show that cou-pling is less likely here than in the preannouncedcase. See that with K = 0, coupling does not occurin Table 7. In the on-the-go case, coupling typicallyoccurs at relatively higher values of launch cost.Effect of consumer heterogeneity: When the market is

composed of only one type of consumer, the firmcan easily optimize its launch cycle to that consumergroup. As Table 8 shows, diversity in valuationsmakes this kind of consumer targeting difficult and,thus, reduces the firm’s profit.

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Lobel et al.: Optimizing Product Launches in the Presence of Strategic Consumers1798 Management Science 62(6), pp. 1778–1799, © 2016 INFORMS

Table 8 Effect of Different Degrees of Consumers’ Heterogeneity

Consumers’ parameters Introduction and purchasing timesFirm’s

‰ Nà v Õ= 4và5 Type 1 Type 2 profit

1 2 12,000 4181121 0 0 0 135 Same as type 1 108,2402 1 410100031410005 4181121 0 0 0 135 Same as type 1 108,2402 1 48100031610005 Every five periods 316191 0 0 0 131135 116,8502 1 46100031810005 61121181 0 0 0 135 316191 0 0 0 135 108,1702 1 44100032010005 8, 16, 24, 34 316191 0 0 0 135 95,0642 1 42100032210005 12, 24, 35 316191 0 0 0 135 85,650

Notes. Parameters are T = 35, c= 0, K = 41000, p= 801000, and Éf = Éc =008. The market size is N1 = N2 = 1 for all cases, with different compositions.

Table 9 Consumers’ Patience and Launch Policy

Consumers’ discount Introduction and purchasingfactor Éc times Firm’s profit

0.70 Every 6 periods 71104060.60 Every 7 periods 51306090.50 Every 8 periods 41031030.40 Every 9 periods 31100060.30 Every 10 periods 2140505

Note. Parameters are T = 45, K = 301000, p = 501000, Éf = 008, c = 0,‰= 1, N1 = 1, and v = 41000.

Effect of consumer patience: For a single-class mar-ket, reduced consumer discount factor reduces the fre-quency at which they purchase and, therefore, lowersthe firm’s profits, as Table 9 shows.

8. ConclusionIn this paper, we study how a technology firm shouldintroduce successive generations of a product overtime to maximize the net present value of its cashflow given that its customers are also making pur-chasing decisions to maximize their own discountedsurpluses. We show that when the firm releases prod-ucts on the go, the technology increments are con-stant in equilibrium. We also show that the firmcan increase its profits between 4% and 12% bycommitting in advance to the next product gener-ation’s technology level after two consecutive, rela-tively close introductions. The optimal preannouncedlaunch strategy involves alternating minor and majortechnology improvement cycles when the consumers’benefit of owning the product (measured by its long-term technology value) is high. This strategy enablesthe firm to anticipate some consumer purchases bypromising those customers that no new products willbe released with a small technology increment, thusreducing their opportunity value of waiting for thenext product release.Both the preannounced and on-the-go launch poli-

cies can be seen as extreme cases of the practices exe-cuted by technology firms in the real world. Microsoft,

Intel, and Apple sometimes announce expected tech-nology levels for their major product releases far inadvance, but they may not do so for the successivegenerations. Concurrently, and resuming the Applestory described in §1, consumers build expectationsbased on the past history of releases and are not sur-prised by new iPhones coming up on the market in asequence of major followed by minor improvements(3G to 3GS, 4 to 4S, 5 to 5S, 6 to 6S), which is not cap-tured by the Markovian foundation of our on-the-gosetting either. Indeed, one could argue that the timelag between the announcement and the major releasein our preannounced setting can be seen as a proxy forthe implicit commitment of not releasing soon after aminor launch. All in all, preannouncement as one pos-sible commitment device is important after releaseswith relatively little technology improvement in orderto convince consumers to purchase regardless. It isparticularly valuable when either the expected rate orthe variance of technology progress are high, sinceconsumers may expect product launches to occur rel-atively often in these two cases.The framework introduced in this paper opens sev-

eral new avenues for potential future work. Oneinteresting direction is empirical: estimating long-term technology values of real products and matchingthese values to their launch policies would allow us tounderstand whether firms are currently successful inmanaging strategic customers. Extending our modelto a competitive setting or to a setting with finite pro-duction capacity would also be important topics forfuture research.

Supplemental MaterialSupplemental material to this paper is available at http://dx.doi.org/10.1287/mnsc.2015.2189.

AcknowledgmentsThe authors are grateful to Yossi Aviv, the associate editor,and three anonymous referees for their constructive feed-back during the review process. I. Lobel thanks the NationalScience Foundation for its support [Grant CCF-1216004],and J. Zhang thanks the National Natural Science Founda-tion of China for its support [Grant 71331004].

ReferencesAdner R, Levinthal D (2001) Demand heterogeneity and technol-

ogy evolution: Implications for product and process innova-tion. Management Sci. 47(5):611–628.

Aviv Y, Pazgal A (2008) Optimal pricing of seasonal products in thepresence of forward-looking consumers. Manufacturing ServiceOper. Management 10(3):339–359.

Aviv Y, Levin Y, Nediak M (2009) Counteracting strategic consumerbehavior in dynamic pricing systems. Netessine S, Tang C, eds.Consumer-Driven Demand and Operations Management Models,International Series in Operations Research and ManagementScience, Vol. 131 (Springer, New York), 323–352.

Bakos Y, Brynjolfsson E (1999) Bundling information goods: Pricing,profits, and efficiency. Management Sci. 45(12):1613–1630.

Dow

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y [2

16.1

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Lobel et al.: Optimizing Product Launches in the Presence of Strategic ConsumersManagement Science 62(6), pp. 1778–1799, © 2016 INFORMS 1799

Balcer Y, Lippman SA (1984) Technological expectations and adop-tion of improved technology. J. Econom. Theory 34(2):292–318.

Bass FM (1969) A new product growth model for consumerdurables. Management Sci. 15(5):215–227.

Bayus BL (1992) The dynamic pricing of next generation consumerdurables. Marketing Sci. 11(3):251–265.

Besbes O, Lobel I (2015) Intertemporal price discrimination: Struc-ture and computation of optimal policies. Management Sci.61(1):92–110.

Borgs C, Candogan O, Jennifer C, Lobel I, Nazerzadeh H (2014)Optimal multiperiod pricing with service guarantees. Manage-ment Sci. 60(7):1792–1811.

Casadesus-Masanell R, Yoffie DB (2007) Wintel: Cooperation andconflict. Management Sci. 53(4):584–598.

Cohen MA, Eliashberg J, Ho T-H (1996) New product development:The performance and time-to-market tradeoff. Management Sci.42(2):173–186.

Correa J, Montoya R, Thraves C (2011) Contingent preannouncedpricing policies with strategic consumers. Working paper, Uni-versity of Chile, Santiago.

Elmaghraby W, Gülcü A, Keskinocak P (2008) Designing optimalpreannounced markdowns in the presence of rational cus-tomers with multiunit demands. Manufacturing Service Oper.Management 10(1):126–148.

Farzin Y, Huisman K, Kort P (1998) Optimal timing of technologyadoption. J. Econom. Dynam. Control 22(5):779–799.

Goemans MX, Skutella M (2004) Cooperative facility locationgames. J. Algorithms 50(2):194–214.

Greer D, Ruhe G (2004) Software release planning: An evolutionaryand iterative approach. Inform. Software Tech. 46(4):243–253.

Hendricks KB, Singhal VR (1997) Delays in new product introduc-tions and the market value of the firm: The consequences ofbeing late to the market. Management Sci. 43(4):422–436.

Karatzas I, Shreve S (1991) Brownian Motion and Stochastic Calculus,2nd ed. (Springer, New York).

Klastorin T, Tsai W (2004) New product introduction: Timing,design, and pricing. Manufacturing Service Oper. Management6(4):302–320.

Kolen A, Tamir A (1990) Discrete Location Theory (John Wiley &Sons, New York).

Kouvelis P, Mukhopadhyay S (1999) Modeling the design qual-ity competition for durable products. IIE Transactions 31(9):865–880.

Krankel RM, Duenyas I, Kapuscinski R (2006) Timing successiveproduct introductions with demand diffusion and stochastictechnology improvement. Manufacturing Service Oper. Manage-ment 8(2):119–135.

Kumar S, Swaminathan JM (2003) Diffusion of innovations undersupply constraints. Oper. Res. 51(6):866–879.

Lai G, Debo LG, Sycara K (2010) Buy now and match later: Impactof posterior price matching on profit with strategic consumers.Manufacturing Service Oper. Management 12(1):33–55.

Lilien GL, Yoon E (1990) The timing of competitive market entry:An exploratory study of new industrial products. ManagementSci. 36(5):568–585.

Liu H, Özer Ö (2009) Managing a product family under stochas-tic technological changes. Internat. J. Production Econom. 122(2):567–580.

Mahajan V, Muller E (1996) Timing, diffusion, and substitu-tion of successive generations of technological innovations:The IBM mainframe case. Tech. Forecasting Soc. Change 51(2):109–132.

Moorthy KS (1988) Product and price competition in a duopoly.Marketing Sci. 7(2):141–168.

Norton J, Bass F (1987) A diffusion theory model of adoptionand substitution for successive generations of high-technologyproducts. Management Sci. 33(9):1069–1086.

Norton J, Bass F (1992) Evolution of technological generations: Thelaw of capture. Sloan Management Rev. 33(2):66–77.

Osadchiy N, Vulcano G (2010) Selling with binding reserva-tions in the presence of strategic consumers. Management Sci.56(12):2173–2190.

Pae J, Lehmann D (2003) Multigeneration innovation diffusion: Theimpact of intergeneration time. J. Acad. Marketing Sci. 31(1):36–45.

Paulson Gjerde KA, Slotnick SA, Sobel MJ (2002) New productinnovation with multiple features and technology constraints.Management Sci. 48(10):1268–1284.

Plambeck E, Wang Q (2009) Effects of e-waste regulation on newproduct introduction. Management Sci. 55(3):333–347.

Ruhe G, Saliu MO (2005) The art and science of software releaseplanning. IEEE Software 22(6):47–53.

Satariano A (2011) Apple falls after wait for iPhone causesmissed estimates. Bloomberg News (October 19), http://www.bloomberg.com/news/articles/2011-10-18/apple-s-results-miss-estimates-as-iphone-sales-fall-short-shares-decline.

Stremersch S, Muller E, Peres R (2010) Does new productgrowth accelerate across technology generations? MarketingLett. 21(2):103–120.

Su X, Zhang F (2008) Strategic customer behavior, commit-ment, and supply chain performance. Management Sci. 54(10):1759–1773.

Wells C (2012) iPhone 5 release date hints dropped by AppleCEO Tim Cook. New York Daily News (July 26), http://www.nydailynews.com/news/money/iphone-5-release-date-hints-dropped-apple-ceo-tim-cook-article-1.1122429.

Wilson LO, Norton JA (1989) Optimal entry timing for a productline extension. Marketing Sci. 8(1):1–17.

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