rev iss web poms 12093 23-5 829. · 2015. 3. 3. · title: rev_iss_web_poms_12093_23-5 829..846...

The Effect of Competition on the Efficient–ResponsiveChoice

Tong WangDecision Sciences, National University of Singapore, Singapore 119245, Singapore, [email protected]

Douglas J. ThomasSmeal College of Business, Pennsylvania State University, University Park, Pennsylvannia 16802, USA, [email protected]

Nils RudiTechnology and Operations Management, INSEAD, Singapore 138676, Singapore, [email protected]

I n determining their operations strategy, a firm chooses whether to be responsive or efficient. For firms competing in amarket with uncertain demand and varying intensity of substitutability for the competitor’s product, we characterizethe responsive or efficient choice in equilibrium. To focus first on the competitive implications, we study a model where afirm can choose to be responsive at no additional fixed or marginal cost. We find that competing firms will choose thesame configuration (responsive or efficient), and responsiveness tends to be favorable when demand uncertainty is highor when product competition is not too strong. Intense competition can drive firms to choose to be efficient rather thanresponsive even when there is no additional cost of being responsive. In such a case, both firms would be better off bychoosing to be responsive but cannot credibly commit. We extend the basic model to study the impact of endogenizedproduction timing, multiple productions and product holdback (or, equivalently, postponed production). For all these set-tings, we find structurally similar results; firms choose the same configuration, and the firms may miss Pareto-improve-ments. Furthermore, through extensions to the basic model, we find that greater operational flexibility can makeresponsiveness look less attractive in the presence of product competition. In contrast to our basic model and other exten-sions, we find it is possible for one firm to be responsive while the other is efficient when there is either a fixed cost orvariable cost premium associated with responsive delivery.

Key words: efficient–responsive; quick response; competitionHistory: Received: July 2012; Accepted: April 2013 by Jay Swaminathan, after 4 revisions.

1. Introduction

Quick response, the ability of a firm to rapidlyrespond to demand requests, has been proposed as abusiness strategy to mitigate the costs of supply–demand mismatch due to volatile market conditions.Fisher et al. (1997) discuss a variety of levers a firmcan employ to increase its ability to respond todemand and supply variability. The essential idea isto increase responsiveness such that firms can post-pone operational commitments until more demandinformation can be obtained. The decision of whetheror when to adopt responsiveness has received andcontinues to receive widespread attention in the oper-ations management literature. In much of this work,there underlies a common wisdom that, all else equal,responsiveness is beneficial, as it provides extra flexi-bility for firms to respond to market changes. Thus,the traditional framework of analyzing the decision

falls into some form of cost–benefit analysis: the costof responsiveness in terms of increased investment incapacity or infrastructure and possibly higher operat-ing costs vs. the benefit of responsiveness in terms ofthe improved matching of supply and demand thatcan occur due to the information gained throughdelayed commitment.In this study we analyze, from a strategic perspec-

tive, the decision of whether to be responsive or not inthe presence of market competition (see Figure 1 for avisual illustration). Our main focus is on the interac-tion between information and competition (the dark-ened arrow in Figure 1), although we address costinteractions in extensions to the basic model. Themain question we address is how competition affectsa firms’ choice between efficient and responsive pro-duction. Motivated by the setting where firms pro-duce branded products that compete in the samemarket, we model competition with partial product

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Vol. 23, No. 5, May 2014, pp. 829–846 DOI 10.1111/poms.12093ISSN 1059-1478|EISSN 1937-5956|14|2305|0829 © 2013 Production and Operations Management Society

substitution. This allows us to explore how the inten-sity of product competition affects the efficient–responsive choice.We first construct a basic game-theoretic model

where two firms produce partially substitutable prod-ucts and compete in a market with a short sellingseason and uncertain demand conditions. Beforedemand conditions are realized, there are two periodsin which the firms may produce. An efficient firm hasto produce in the first period due to its longer pro-duction lead time, while a responsive firm delays theproduction to the second period. New informationabout market demand becomes available after thefirst period, so it is only useful to firms that areresponsive. In our model, firms first decide whetherto be efficient or responsive (the strategic stage) andthen choose production quantities in the correspond-ing period (the tactical stage). A responsive firm facesless uncertainty and is able to obtain extra value ofinformation, while an efficient firm enjoys the value ofcommitment due to moving first. The decision ofwhether to be responsive or efficient is thus deter-mined by trading off the value of information and thevalue of commitment.In our basic model, we find that when there is no

cost premium associated with responsiveness, beingefficient can be a dominant strategy even though prof-its for both firms are higher under responsiveness.This is the case when market uncertainty is not toolarge while market competitiveness is high. On theother extreme, when uncertainty is high but competi-tiveness is low, being responsive becomes the domi-nant strategy. There exists a third case in betweenwhen firms prefer choosing the same strategy: bothbeing responsive and both being efficient are the twoNash equilibria.

In constructing the basic model, we make a set ofassumptions in order to highlight the key result parsi-moniously. To test the robustness of the findings, werelax these assumptions in the latter part of the studyby considering an endogenized timing game wherefirms freely choose their lead time, a multi-productionmodel that allows a responsive firm to produce inmul-tiple batches in both periods, a holdback model thatallows firms to withhold previously committed quan-tity in the selling season, and a model where respon-siveness comes at a cost. The qualitative structure ofthe above result remains the same except that whenthere is cost difference between efficient and respon-sive production. More importantly, by comparing theextensions with the basic model, we find two rathercounter-intuitive results: allowing the responsivefirms to produce in both periods reduces the attractive-ness of responsiveness, and allowing the efficient firmto withhold committed quantity reduces the attractive-ness of being efficient. This suggests that extra opera-tional flexibility can actually harm the firms in such acommitment game. We discuss the managerial impli-cations of these findings at the end of this study.The study is organized as follows. We briefly

review related literature in section 2. In section 3, wedevelop the basic model and analyze the solutions indetail. Extensions to the basic model are discussed insection 4. Section 5 concludes the study with discus-sions on the managerial implications. Proofs and deri-vations for the basic model are in the Appendix.Proofs related to model extensions are available in thesupporting information. Code for all numericalexperiments is available at https://github.com/tong-wang/Efficient-Responsive.

2. Literature Review

Our work is related to three streams of research. Inthe operations management literature, Fisher andRaman (1996) and Iyer and Bergen (1997) are amongthe first works to investigate the impact of adopting aquick response strategy. Based in part on this work,Fisher (1997) presents a framework for matchingdemand-related product characteristics (functional orinnovative, in terms of level of demand uncertainty,customer service expectations, relative importance ofcost efficiency, etc.) with responsive or efficient sup-ply chains. Lee (2002) extends this framework by con-sidering how characteristics of the supply process(stable or evolving) affect the efficient–responsivechoice. Randall and Ulrich (2001) and Randall et al.(2003) investigate the efficient–responsive choiceempirically, providing some evidence that correctlymatching product characteristics with responsiveor efficient supply chains leads to improved firmperformance. Ray et al. (2005) develop a model that

Information

Cost

Market Competition

Figure 1 Three Factors Affecting the Choice between Efficient andResponsive Production

Wang, Thomas, and Rudi: Efficient–Responsive Choice830 Production and Operations Management 23(5), pp. 829–846, © 2013 Production and Operations Management Society

further incorporates high and low price sensitivitywith supply chain choice. Wang et al. (2012a) analyzehow to optimally design a portfolio of efficient andresponsive suppliers and how to order from thesesuppliers dynamically as more information isobserved. These studies emphasize the trade-offbetween value of information and cost of responsive-ness, while we investigate how competition affectsthe efficient–responsive choice.The second stream is the Industrial Organization

literature (Vives 2000, section 7), particularly the com-mitment models. Saloner (1987) studies a Cournotmodel with two production periods and shows thereis a continuum of subgame perfect Nash equilibriaincluding the Stackelberg outcome. Pal (1991) intro-duces cost differentials and finds leader–followerequilibria when cost decreases over time. Maggi(1996) incorporates uncertainty into Saloner’s modeland identifies asymmetric leader–follower equilibria.This stream of research emphasizes the special struc-tures of the equilibrium outcome. Built on these mod-els, our research focuses on the strategic implicationsof being efficient or responsive.The third stream, emerging more recently, consid-

ers the effect of competition on strategic choices inoperations management contexts. Van Mieghem andDada (1999) show how competition affects firms’choices of price and production postponement.Cachon and K€ok (2010) investigate the impact ofmanufacturer competition on coordinating contractsoffered to a common retailer, while Zhao (2008) inves-tigates how competition affects coordinating contractswhen a single manufacturer sells to competing retail-ers. Caro and de Albeniz (2010) also study the impactof retail competition and adoption of quick response.In their setting, retailers see unmet demand from theircompetitors. Krishnan et al. (2010) analyze competingsuppliers’ incentives to reduce lead time when a com-mon retailer can control sales effort on their products.Anand and Girotra (2007) study the effect of competi-tion on a firm’s decision to delay product differentia-tion, and Goyal and Netessine (2007) on productionflexibility. Wang et al. (2012b) study inventory com-petition between an original equipment manufacturer(OEM) and a supplier who can also compete in themarket. Their work provides insights regarding howthis particular kind of competition affects tradebetween the OEM and its supplier, including theimpact on transfer pricing.Lin and Parlakt€urk (2012) and Wu and Zhang

(2013) both study settings where firms engage ininventory competition and must choose whether ornot to adopt responsive sourcing. In Wu and Zhang(2013), motivated by the offshoring vs. domestic pro-duction setting, firms choose to be either efficient orresponsive and have just one ordering opportunity. In

addition, they investigate the impact of whether ornot a firm would choose to acquire updated demandinformation if it were costly to do so. Lin and Par-lakt€urk (2012) investigate how a manufacturer sellingthe same product to two retail competitors wouldoffer and price a quick response option. In their set-ting, the products are homogenous and thus puresubstitutes. Some key findings are that

(i) the manufacturer may benefit from offeringquick response to only one of their two retail-ers,

(ii) the retailer who is offered quick response maybe worse off, and

(iii) neither of these results hold in the monopolysetting.

That is, retail competition may discourage the man-ufacturer from making quick response broadly avail-able. Similar to these works, we are interested in howcompetition affects a manufacturer’s choice to offerresponsiveness. In contrast to both Lin and Parlakt€urk(2012) and Wu and Zhang (2013), however, we modelthe efficient–responsive choice for competing firmsselling differentiated products that may not be puresubstitutes. As our results indicate, the intensity ofproduct competition relative to the demand variabil-ity drives the efficient–responsive choice in this set-ting. Moreover, we extend the basic model to provideunique features such as a production timing gamewith continuous strategy space, multiple productionopportunities, and an explicit analysis of productholdback.

3. The Basic Model

In this section, we construct a basic model to capturethe trade-off between value of information (VOI) andvalue of commitment (VOC) and derive the maininsights analytically.

3.1. Model Settings3.1.1. Market Structure. There are two risk-neu-

tral firms (1 and 2) supplying (partially) substitutableproducts to a market and competing in quantity. Theaggregated response of the market is obtained byconsidering the optimal consumption made by a rep-resentative consumer with quadratic utility (Vives2000, section 6.1):

Uðq1; q2Þ ¼ nðq1 þ q2Þ � 12ðaq21 þ 2bq1q2 þ aq22Þ; ð1Þ

where ξ is a random number representing the over-all uncertainty in the market, qi is the quantity sup-plied to the market by firm i, a is normalized to 1,without loss of generality, and 0 ≤ b ≤ 1 captures

Wang, Thomas, and Rudi: Efficient–Responsive ChoiceProduction and Operations Management 23(5), pp. 829–846, © 2013 Production and Operations Management Society 831

the substitutability between the two products (whenb = 0 the two products are mutually independent;when b = 1 they are perfect substitutes). We assumethe two products are subject to the same marketuncertainty and price sensitivity both ex ante and expost. This allows us to model the continuous changefrom perfect substitutable products to mutuallyindependent products and a continuous change inthe market uncertainty, focusing on how thesefactors affect the efficient–responsive choice.The representative consumer maximizes her

surplus,

CS ¼ Uðq1; q2Þ � p1q1 � p2q2; ð2Þ

and this leads to the inverse demand function facedby the two firms, which is standard in the econom-ics and marketing literature (Christen et al. 2009,McGuire and Staelin 1983, to name a few):

pi ¼ n� qi � bqj; i; j 2 f1; 2g; i 6¼ j: ð3Þ

Later, following Singh and Vives (1984), we useEquation (2) to calculate the impact of firms’ decisionson consumer and total surplus.

3.1.2. Information Structure. The time horizon isassumed to be a continuum [0, 1], where time 0 is theearliest epoch a quantity decision can be made andtime 1 is when demand is realized and the marketclears. At time 0, the market condition ξ is unknown.We model it as a continuous random variable withp.d.f. f(ξ) and c.d.f. F(ξ) defined on a non-negativesupport. The mean and variance of ξ are given by land r2, respectively. For the basic model, we makeno assumption on how the knowledge about ξevolves over the horizon; all that we need to assumeis that at time 1, the realization of the ξ can beobserved, and the uncertainty in the market is com-pletely resolved.

3.1.3. Operational Strategies. The firms play atwo-stage game. The first stage is the strategic choiceof the production technologies. There are two technol-ogies available: a firm can be either efficient (E) orresponsive (R). The decisions are made at the verybeginning before any information is observed. Thesecond stage is the tactical decision of how much toproduce. The firms decide their production quantityqi � 0 some time before the market starts, and a unitcost c (we assume c < l to avoid trivial cases) isincurred. The actual timing of the quantity decisionsis determined by the production technology adopted.Efficient production requires longer lead time, so thequantity decisions need to be made earlier. A respon-sive firm can produce with a shorter lead time andtherefore is able to delay the quantity decision and

acquire additional information about the marketcondition ξ. The exact timing of quantity decisions isspecified later in each of the scenarios. The strategyadopted may also affect the firms’ production cost.All the parameters and actions made in earlier

stages are public information to both players.

3.1.4. Assumptions. The following assumptionsare made in the basic model.

ASSUMPTION 1 (0–1 LEAD TIME). A responsive firm canproduce with zero lead time and therefore is able to delaythe quantity decision until time 1 when the realization ofmarket condition ξ is observed and all the uncertaintyis resolved. The lead time of an efficient firm is 1, so theproduction quantity has to be determined at time 0 underuncertainty.

ASSUMPTION 2 (ONE-SHOT PRODUCTION). Both types offirms delay the quantity commitment as much as possibleand produce only once at the latest possible time (deter-mined by the lead time associated with the strategyadopted).

ASSUMPTION 3 (NO HOLDBACK). All products producedare released to the market.

ASSUMPTION 4 (NO COST DIFFERENCE). Responsivenesscomes at no extra fixed or marginal cost.

We start with these assumptions in order to keepthe model parsimonious and focus on the key trade-off. For example, the assumption of costless respon-siveness helps us focus on the interaction betweenVOI and VOC and avoid the distortion from the thirdeffect of cost disadvantage. Nevertheless, in the nextsection, we relax these assumptions by consideringproduction timing, multiple productions, productholdback, and production cost differences and justifythe robustness of the results obtained from the basicmodel.

3.2. Tactical Decisions: Production QuantitiesWe focus on Markov Perfect Equilibria and solve thegame by backward induction. We first study optimalproduction quantities for both firms, assuming theirproduction strategies have been determined. Thereare three scenarios to be considered:

(i) both are efficient (E–E);(ii) both are responsive (R–R); and(iii) one is efficient and the other is responsive

(E–R).

Figure 2 graphically depicts these scenarios. Whenthe two firms choose the same strategy, the problemis in the form of simultaneous Cournot quantity


competition (with or without uncertainty). When theychoose different strategies, the problem becomes aStackelberg-type game where the efficient firm is theStackelberg leader, deciding quantity first; the respon-sive firm is the second-mover but enjoys the benefit ofsuperior information.

3.2.1. Scenario I: E–E. The firms simultaneouslymake the quantity decisions at time 0. For firm i,

piðqi; qjÞ ¼ E½ðpiðqi; qj; nÞ � cÞqi�¼ ðl� qi � bqj � cÞqi; i; j 2 f1; 2g; i 6¼ j:

ð4ÞAs the uncertainty does not affect the expected

profit, we have the standard Cournot best response

qiðqjÞ ¼ðl� c� bqjÞþ

2; ð5Þ

resulting in a unique and symmetric Nash equilib-rium

q1 ¼ q2 ¼ qEjE ¼ l� c2þ b : ð6Þ

Here and hereafter, we use superscript S1jS2 ,S1; S2 2 fE;Rg; to denote the outcome of a firmchoosing strategy S1 given the other firm chooses S2,and superscript S1�S2 for the outcome of the scenariowith one firm being S1 and the other being S2.At this equilibrium, the expected profit of each firm,

the expected consumer surplus, and total surplus aregiven by

pEjE ¼ l� c2þ b

� �2; CSE�E ¼ ð1þ bÞpEjE;

TSE�E ¼ ð3þ bÞpEjE:ð7Þ

3.2.2. Scenario II: R–R. Both firms first observe ξand then decide their quantities simultaneously attime 1. The profit, for a given ξ, is

piðqi; qj; nÞ ¼ ðn� qi � bqj � cÞqi; i; j 2 f1; 2g; i 6¼ j;ð8Þ

so the best response is

qiðqj; nÞ ¼ðn� c� bqjÞþ

2: ð9Þ

The unique Nash equilibrium is then

q1ðnÞ ¼ q2ðnÞ ¼ qRjRðnÞ ¼ ðn� cÞþ

2þ b :

At time 0 (before observing ξ), the expected outputquantity by each firm is

qRjR ¼ E ðn� cÞþ

2þ b� �

; ð10Þ

and the expected profit is

pRjR ¼ E ðn� cÞþ

2þ b� �2" #

: ð11Þ

The expected consumer surplus and total surplusare ð1þ bÞpRjR and ð3þ bÞpRjR, respectively.

3.2.3. Scenario III: E–R. Suppose firm 1 is effi-cient and firm 2 is responsive. Now we have a Stackel-berg setting where firm 1 first decides quantity q1 attime 0, then firm 2 makes its quantity decision at time1 after observing q1 and the market condition ξ. Attime 1, firm 2 solves a deterministic problem

p2ðq1; q2; nÞ ¼ ðn� q2 � bq1 � cÞq2; ð12Þand produces

q2ðq1; nÞ ¼ ðn� c� bq1Þþ

2: ð13Þ

Firm 1 makes the quantity decision, anticipatingfirm 2’s response. The expected price of product 1 for

q1

q2

Firm 1

Firm 2

Time 0

Time 1

Scenario I: E-E

q1

q2

Time 0

Time 1

Scenario II: R-R

q2

Time 0

Time 1

Scenario III: E-R

q1

Figure 2 Scenaroius in the Basic Model


given q1 and ξ is

p1ðq1; q2ðq1; nÞ; nÞ ¼ n� q1 � b ðn� c� bq1Þþ

2: ð14Þ

Taking expectation with regard to ξ, we have theexpected price as a function of q1:

p1ðq1Þ ¼ E½p1ðq1; q2ðq1; nÞ; nÞ�

¼Zbq1þc0

ðn� q1ÞdFðnÞ

þ 12

Z1bq1þc

ð2� bÞn� ð2� b2Þq1 þ bc� �

dFðnÞ:

Firm 1 maximizes

p1ðq1Þ ¼ E ðp1ðq1; q2ðq1; nÞ; nÞ � cÞq1½ �; ð15Þwhich is concave. The optimal q1 satisfies thefollowing first-order condition

Zbq1þc0

b

2n� c� 2bq1½ �dFðnÞ þ 2� b

2ðl� cÞ

�ð2� b2Þq1 ¼ 0:

ð16Þ

The first-order derivative is decreasing in q1, goesto ∞ as q1 ! �1, and goes to �∞ as q1 ! 1. So, theoptimal q1 exists and is unique. Also, it is straightfor-ward to show that the optimal q1 is bounded above by2� b=½2ð2� b2Þ�ðl� cÞ, which is the Stackelbergquantity without uncertainty.Let qEjR denote the quantity that satisfies the above

first-order condition (16). Once it is obtained, we canfind numerically the quantity for the responsive firmqRjE by Equation (13), the expected profits pEjR byEquation (15) and pRjE by Equation (12), and also theconsumer surplus CSE�R and total surplus TSE�R.

3.3. Strategic Decisions: Efficient or ResponsiveAt the strategic level, the firms decide whether to beefficient or responsive based on the optimal expectedprofits obtained from the tactical subgames pEjE, pRjR,pEjR, and pRjE.As we do not have explicit analytical expressions

for the profits in the E–R scenario, it is difficult to ana-lyze the strategic decisions by directly comparingthese profits. In the following, we first consider thesituation where the uncertainty is sufficiently small toallow explicit analytic solutions to be obtained. Wethen investigate the more general setting numerically.

3.3.1. Bounded Uncertainty. We adopt a tradi-tional approach (Van Mieghem and Dada 1999,

p. 1638) by assuming the uncertainty is bounded suchthat the probability that the realized market price isless than the marginal cost is negligible. As a result, itis always profitable for the second-mover to enter themarket and produce a positive quantity. This assump-tion helps avoid the kink in the response functions(eliminate the þ in Equations (10), (11), (13), (14), andthe integral term in Equation (16)) and obtain analyticsolutions.The results are listed in Table 1, and detailed deri-

vations are delegated to the Appendix.We now define the following measures for the

value of information and the value of commitmentand will show later that the firms’ strategic choicesonly depend on the relative magnitude of these mea-sures.

DEFINITION 1. VOI :¼ r2 is a measure of the value ofthe additional information acquired if a firm choosesto be responsive instead of efficient.

DEFINITION 2. VOCE :¼ b3ð16�8b2�b3Þ4ð2�b2Þ2ð2þbÞ2 ðl� cÞ

2 is a mea-

sure of the value of early commitment if the otherfirm is efficient.

DEFINITION 3. VOCR :¼ ½b4=8ð2� b2Þ�ðl� cÞ2 is ameasure of the value of early commitment if theother firm is responsive.

With these definitions and the profit expressionsfrom Table 1, we can write the net change in profitdue to switching from efficient to responsive(depending on the other firm’s choice) as

pRjE � pEjE ¼ 14½VOI � VOCE�; ð17Þ

pRjR � pEjR ¼ 1ð2þ bÞ2 ½VOI � VOCR�: ð18Þ

LEMMA 1. For 0 ≤ b ≤ 1, the following properties hold:

(i) VOCR � 0 and VOCE � 0;(ii) VOCR and VOCE are increasing in b;(iii) VOCR � VOCE.This leads to the following proposition.

Table 1 Game Output with Bounded Uncertainty

I: E–E II: R–RIII: E–R

E R

Expectedquantity (q)

l�c2þb

l�c2þb ð2�bÞðl�cÞ2ð2�b2Þ

ð4�2b�b2Þðl�cÞ4ð2�b2Þ

Expectedprofit (p)

ðl�cÞ2ð2þbÞ2

ðl�cÞ2þr2ð2þbÞ2

ð2�bÞ2ðl�cÞ28ð2�b2Þ

ð4�2b�b2Þ2ðl�cÞ216ð2�b2Þ2 þ

r24


PROPOSITION 1. At the strategic stage the game can havethe following possible outcomes:

(i) R is a dominant strategy if VOI [ VOCE;(ii) E is a dominant strategy if VOI\VOCR;(iii) E–E and R–R are the two Nash equilibria if

VOCR � VOI � VOCE.The asymmetric equilibrium E–R is not possible, asVOCR � VOCE.

What drives different game outcomes here is therelative difference between the value of informationfrom delayed commitment as a function of r2 and thevalue of commitment as a function of the product sub-stitutability b. Figure 3 plots the firms’ strategicchoices on the two-dimensional b � r2 plane. In thisand similar figures later in the study, we fix l = 10,c = 1.The two curves VOCE and VOCR partition the

plane into three parts, corresponding to the threeoutcomes, respectively. In the upper-left region, theuncertainty effect (VOI) dominates the strategiceffect (VOCR and VOCE). Both firms choose to beresponsive in equilibrium, which is consistent withthe conventional wisdom. In the lower-right region,we have the E–E outcome. It suggests that, even ifresponsiveness is free, there can be cases where thevalue of information gained is dominated by thevalue of commitment lost (VOI\VOCR suggestsVOI\VOCE by Lemma 1). Note that this is forpurely competitive reasons that firms might prefernot to be responsive. When there is no competition,b = 0, and there is no cost premium for providing

responsiveness, both manufacturers choose respon-siveness. Moreover, as we can see from Table 1,pEjE � pRjR, which means that although E turns outto be a dominant strategy, R–R is a Pareto-improv-ing outcome compared to E–E. This replicates theclassic prisoner’s dilemma. The third case gives ustwo Nash equilibria, R–R and E–E. The two firmsprefer to adopt the same strategy; no one has incen-tive to deviate unilaterally.The fact that VOCR � VOCE indicates that the

strategic value of early commitment is greater whenthe other firm is also committing early. As we see inEquation (17), a firm is willing to move from effi-cient to responsive when the other firm is efficient ifand only if VOI � VOCE. The resultant asymmetric(E–R) situation cannot be sustained because in thiscase, VOI � VOCE � VOCR, which implies Equation(18) must also be positive. This means if it is valu-able for the first of two efficient firms to deviate andbecome responsive, it must be the case that thesecond firm wants to follow, leading to the R–Requilibrium.Next, we examine how different market conditions

affect the efficient–responsive choice.

COROLLARY 1. Responsiveness is more appealing

(i) when more uncertainty can be resolved (larger r2);(ii) when market size l is smaller;(iii) when product substitutability b is lower.

Existing research suggests that responsiveness ismost beneficial when the market demand is highlyuncertain and when the market competition is intense(Gerwin 1993, Wharton and White 1988). The first halfis confirmed in our analysis, while the second halfdeserves more discussion. If the degree of competi-tion is measured by the market potential l, what weobserve is consistent with the traditional wisdom:responsiveness is more appealing when market size issmaller. However, product substitutability b is argu-ably a better measure of competition. We find thatcontrary to the traditional wisdom, a higher b reducesfirms’ incentive to be responsive because it increasesthe value of commitment. When the products aremutually independent (no competition), the firms willalways choose to be responsive. On the other extreme,when the two products are perfect substitutes (b = 1),the intense market competition makes the value ofcommitment strongest, discouraging firms fromadopting responsiveness. This is in a sense comple-mentary to the Fisher (1997) framework in that wemight expect a more innovative product to be subjectto not only higher demand uncertainty but also lesscompetition (lower b), and therefore be a better matchwith a responsive strategy.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14

16

18

20

b

VO

I ( σ

2 )

VOCR

R−R

E−E

R−R or E−E

VOCE

Figure 3 Firms’ Strategic Choices in Equilibrium under BoundedUncertainty (l = 10,c = 1)


3.3.2. Numerical Demonstration of the GeneralCase. In order to obtain the analytic solutions inTable 1, we assumed the variance was bounded.Here, we solve the strategic decisions numericallyand plot the equilibrium choices for different combi-nations of market volatility (r2) and market competi-tion (b). In all the following numerical examples, weassume n � Nðl; r2Þ. Figure 4(a) plots both thenumerical result (in solid lines) and the result sug-gested by the approximation assuming boundeduncertainty (in dashed lines). The two solid linespartition the strategy space in a qualitatively similarmanner. Note that we still use VOCE and VOCR tolabel the partitioning lines obtained numerically;hereafter the labels no longer follow Definitions 2and 3.Figure 4(b) shows the socially efficient strategies

that maximize the sum of both firms’ profits and con-sumer surplus. From the social point of view, R–Rshould be adopted if uncertainty is high or substitu-tion is low (the upper-left, shaded area), and E–Rotherwise (the lower-right, not-shaded area). When itis on the lower right corner, firms’ strategic choiceE–E is different from the socially preferred choiceE–R, leading to the loss of social welfare.

4. Relaxing Assumptions

In this section, we relax Assumptions 1–4 one by one.

4.1. Game with Endogenous TimingIn the basic model the firms are facing a binary choice:to produce either at time 0 or time 1. Now we relax

this assumption by endogenizing the lead times: firmschoose their production technology with a lead timeon the continuum [0, 1]. At the strategic stage, thestrategy space is no longer {E,R} but the continuum[0, 1], while at the tactical stage, firms still choosequantities to maximize expected profits given technol-ogy choices.In order to study the timing decision, we need to

specify how knowledge about the market condition ξevolves over the planning horizon [0, 1]. Let {X(t),0 ≤ t ≤ 1} be a stochastic process representing thecommon information flow the firms can observeover time. At time 0, with X(0) being given, E[ξ|X(0)]= l and Var½njXð0Þ� ¼ r2. We assume the knowledgeimproves (strictly) over time, that is, Var[ξ|X(s)] >Var[ξ|X(t)] for all s < t. At time 1, Var[ξ|X(1)] = 0 andthe uncertainty in the market is completely resolved.As choosing production technology is a long-term

decision, we focus on open-loop Nash equilibria ofthe timing game, where firms decide when to commitat the very beginning without dynamically respond-ing to the opponent’s move.

PROPOSITION 2. (0,0) is the only possible pure-strategyopen-loop Nash equilibrium in the timing game.

The intuition behind this result is that, given a pro-duction timing decision t for a firm, the other firm canundercut by choosing t � d for some arbitrarily smalld, gaining the first mover advantage and acquiringalmost the same amount of market information. Thisincentive drives the two firms undercutting eachother until they reach (0,0) in the end. This suggests

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14

16

18

20

b

VO

I ( σ

2 )

(a) Firms’ Strategic Choices

VOCR

R−R

E−E

R−R or E−E

VOCE

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14

16

18

20

b

VO

I ( σ

2 )

(b) Socially Efficient Strategies

VOCR

VOCE

E−RR−R

Figure 4 Firms’ Strategic Choices in Equilibrium and Socially Efficient Strategies for the Basic Model: (a) Firms’ Strategic Choices; (b) SociallyEfficient Strategies


that allowing the firms to freely choose their lead timewill not help solve the dilemma in the basic model;on the contrary, the timing flexibility makes thingsworse—both firms stick to being efficient regardlessof market uncertainty and competition intensity,which is a socially inefficient equilibrium.

4.2. Multiple ProductionsThe second assumption in the basic model is thatresponsive firms only make one single batch produc-tion at the latest possible time (t = 1). We have shownhow they may suffer from this delayed commitment.In a more general setting, what responsiveness offersis flexibility in production timing, as a shorter leadtime allows for multi-batch production in response tonew information. One may expect that responsivefirms can improve their payoff by also committingsome quantity at time 0 and then making anotherbatch at 1 when the market condition ξ is observed(producing at a time other than 0 and 1 is possible butclearly makes no sense). By doing this, the responsivefirm might be able to overcome the negative strategicimpact and still take advantage of the superior infor-mation. In this section, we study such problems andshow that multiple productions do not change thefindings in the basic model.Again we start from the tactical decisions on output

quantities in the three scenarios denoted E–Em, R–Rm, and E–Rm (Figure 5).

4.2.1. Scenario IV: E–Em. Efficient firms have along production lead time and can only produce onceat time 0. This scenario is the same as Scenario I (E–E).

4.2.2. Scenario V: R–Rm. When both firms areresponsive, both could produce some quantity (q1; q2)at time 0 to occupy the market and preempt the oppo-nent and, if necessary, increase the (cumulative)quantity to Q1;Q2 at time 1 when more information isavailable. Maggi (1996) studies a similar problem,although the focus is on the asymmetric equilibriaobtained in the symmetric game.

Q1 and Q2 are straightforward to characterize whenthe signal realization is given (see Supporting Infor-mation), so in the following we focus on the quantityq1; q2 at time 0.

PROPOSITION 3. There are three possible equilibria in theR–Rm scenario:

(i) When uncertainty is high, there is a symmetricNash equilibrium q1 ¼ q2 ¼ 0.

(ii) When uncertainty is low, there are two asymmetricNash equilibria: either of the firms produces a posi-tive quantity qRjRm that solves

Zbqþc0

ðn� c� 2qÞ dFðnÞ

þZð2þbÞqþc

bqþc

2� b2

ðn� cÞ � ð2� b2Þq� �

dFðnÞ ¼ 0;ð19Þ

and the other firm produces 0. Moreover, qRjRm is lessthan qEjR in the basic model.

When subject to high market uncertainty, bothresponsive firms will predictably give up the optionof producing early and partially staking out the mar-ket even if they are allowed to do so, as the value ofinformation outweighs the value of commitment. Thisresult is qualitatively consistent with the basic modelwhere high uncertainty results in the value of infor-mation dominating the value of commitment, leadingboth firms to choose responsiveness. When uncer-tainty is low, however, only one of the firms will takethe Stackelberg leader position in equilibrium andproduce qRjRm in the first period. The reason only onefirm chooses to produce early is that the firm takingthe leader position is able to produce enough at time0 to reduce the marginal value of commitment for thefollowing firm to the point where the following firmdoes not benefit from early production. It can also beshown by comparing Equation (19) with Equation(16), the first order condition in Scenario E–R, that

q1 q1

q2

Firm 1

Firm 2

Time 0

Time 1

Scenario IV: E-Em

Q1

Q2

Time 0

Time 1

Scenario V: R-Rm

Time 0

Time 1

Scenario VI: E-Rm

q1

q2 Q2q2

Figure 5 Scenarios in the Multi-production Model


qRjRm is less than or equal to qEjR, the Stackelbergleader quantity the E firm produces in the E–Rscenario. This is intuitive, as now the leader has theoption to produce later in the second period.The possibility of the two asymmetric equilibria in

the R–Rm scenario creates a challenge in analyzingfirms’ strategic choice: a firm committing to beresponsive and entering the R–Rm scenario does notknow whether it will be the leader, producing strictlypositive qRjRm, or the follower, producing nothing attime 0. In the numerical demonstration below, weassume that firms are equally likely to be the followeror the leader.

4.2.3. Scenario VI: E–Rm. The model setting isthe same as that in Scenario III, except that firm 2,the responsive firm, can now produce q2 at time 0and has the option to produce another batch andincrease its supply to Q2 at time 1. The followingproposition shows that even if the responsive firm isgiven such an option to produce at time 0, in equilib-rium it will choose to produce nothing if its oppo-nent is efficient.

PROPOSITION 4. The responsive firm in the E–Rm equi-librium will not produce at time 0, that is, q2 ¼ 0. Theproblem reduces to Scenario III (E–R).

As the responsive firm has the flexibility of pro-ducing in both periods, it may seem like it can do at

least as well as the efficient firm. In this game-theo-retic setting, however, a responsive firm’s threat tomimic the action of the efficient firm is not credible,as the efficient firm knows that the responsive firm isbetter off not producing early. This can be seen fromthe profit function of the responsive firm (see proofof Proposition 4), which is concave and decreasing inq2; thus, for any given q1, q2ðq1Þ should always be setto zero and the production should be done in onebatch later at time 1. Having extra flexibility andhaving the other player know about this extra flexi-bility make the firm unable to commit in a credibleway.

4.2.4. Numerical Demonstration. Figure 6(a)compares firms’ choices in the single- (dashed lines)and multi-production (solid lines) models (everythingelse being the same). In both models the space is parti-tioned by two lines into three parts: R dominant, R–Ror E–E, and E dominant, from top to bottom. As theE–Em scenario is the same as E–E from the basicmodel, the VOCE line from the base model remainsthe same. The difference is the position of the line sep-arating E–E from the R–R or E–E space, VOCRm,which is higher than VOCR from the basic model,suggesting that E–E is more likely in the multiple-production model.It may initially seem that the possibility of multiple

productions would increase the adoption of theresponsive technology. As Figure 6(a) shows though,

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14

16

18

20

b

VO

I ( σ

2 )


R−R

E−E

R−R orE−E

VOCE

VOCR

VOCRm

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14

16

18

20(b) Socially Efficient Strategies

b

VO

I ( σ

2 )

E−RR−R

VOCE

VOCRm

Figure 6 Firms’ Strategic Choices in Equilibrium and Socially Efficient Strategies for Multi-production: (a) Firms’ Strategic Choices; (b) SociallyEfficient Strategies


it is actually the opposite. Essentially, introducingmulti-production expands the action space of theresponsive firms such that they can produce in bothperiods and possibly mimic the action of efficientfirms. However, in such a commitment game, havinga large action space may not be helpful, as it harmsthe credibility of commitment. Another concern mightbe that, because of the existence of multiple equilibriain the R–Rm subgame, firms are unable to predictwhether they will end up being the leader who pro-duces qRjRm or the follower who produces nothing.This dampens the attractiveness of being responsive.Figure 6(b) shows the socially efficient strategies

under multiple productions. The results are qualita-tively similar to the results from the basic modeldepicted in Figure 4(b).

4.3. Holdback or Postponed ProductionAs seen in our earlier results, a responsive firm maysuffer from its inability to stake out part of the mar-ket. Here, we investigate whether or not a firm canmitigate this strategic disadvantage by producingearly and then choosing to hold product back afterthe market demand update. Holdback can be viewedas the opposite of the multiple-production case. Thelatter allows responsive firms to produce at time 0and increase the quantity at time 1, while the formerallows efficient firms to produce at time 0 and reducethe quantity supplied to the market at time 1 bywithholding. We proceed by analyzing holdback andnote at the end of this section how holdback can beviewed as equivalent to postponed production.We assume withheld units are salvaged at price

s ≤ c. If s = c, products can be fully salvaged, and effi-cient firms can produce infinity to cover any upsidedemand risk. If s = 0, no cost can be recovered byholdback, but extra units can still be disposed for freewhen necessary. If s?�∞, holdback makes noeconomic sense, and the problem reduces to thebasic model. The holdback scenarios are depicted inFigure 7.

4.3.1. Scenario VII: E–Eh. The two firms produceQ1;Q2 at time 0 and decide how much to actually sup-ply to the market (q1 � Q1, q2 � Q2) at time 1.

PROPOSITION 5. The unique symmetric Nash equilibriumis Q1 ¼ Q2 ¼ QEjEh, where QEjEh solves

Z1ð2þbÞQþs

½n� s� ð2þ bÞQ�dFðnÞ ¼ c� s: ð20Þ

4.3.2. Scenario VIII: R–Rh. Responsive firms donot need to hold back and salvage, so this scenarioreduces to the basic R–R scenario.

4.3.3. Scenario IX: E–Rh.PROPOSITION 6. At time 0, the efficient firm producesQ1 ¼ QEjRh, which is equal to either Qa or Qb, which-ever maximizes the expected profit. Qa � ðc� sÞ=ð2� bÞis the solution to

ZbQþc2Qþs

ðn� s� 2QÞ dFðnÞ

þZ1

bQþc

2� b2

n� sþ b2c� ð2� b2ÞQ

� �dFðnÞ ¼ c� s;

and Qb [ ðc� sÞ=ð2� bÞ is the solution toZ1

ð2þbÞQþ2s�bc2�b

2� b2

n� sþ b2c� ð2� b2ÞQ

� �dFðnÞ ¼ c� s:

4.3.4. Numerical Demonstration. Figure 8 dem-onstrates the firms’ choices in equilibrium and thesocially preferred choices for different salvage

Firm 1

Firm 2

Time 0

Time 1

Scenario VII: E-Eh

Time 0

Time 1

Scenario VIII: R-Rh

Time 0

Time 1

Scenario IX: E-Rh

Q1 q1q1

q2 q2

Q1 q1

Q2 q2

Figure 7 Scenarios in the Holdback Model


value s. Again it is qualitatively similar to what wehave in the basic model. The lines VOCEh and VOCRh

divide the strategy space into R–R, either R–R or E–E,and E–E regions, and the socially efficient outcome iseither R–R or E–R.With s?�∞ we have the same result as the basic

model. As s increases, the R–R region expands. High sbenefits efficient firms in the sense that they face lessdownside risk, but at the same time, it underminesthe power and credibility of their commitment. Toone extreme, when s = c, an efficient firm producesinfinity at time 0 but can only sells a Cournot quantityat time 1. In this case, they completely lose the strate-gic benefit of commitment.To demonstrate this intuition, we plot Figure 9

showing the quantities QE and qE by the efficient firm1 and qR by the responsive firm 2 in Scenario E–Rh asa function of the salvage value s. Other parametersare l = 10, c = 1, r2 ¼ 9; and b = 1. When s is low,salvage is costly, so there is very little holdback (QE

is close to qE.) Also QE and qE are close to the deter-ministic Stackelberg quantity (¼ ð2� bÞ=½2ð2� b2Þ�ðl � cÞ ¼ 4:5 in this setting), suggesting the efficientfirm benefits more from commitment. Larger valuesof s induce larger initial quantities QE but also largequantity held back, QE � qE. The final outputs fromthe efficient and responsive firms are getting closer tothe Cournot quantity (= (l � c)/(2 + b) = 3 in thissetting) as s gets closer to c.We note here that although the model in this sub-

section deals with the option of holdback, it can beinterpreted as a model for postponed production (for

s ≥ 0). Efficient firms essentially split the productionprocess into two steps. The first step needs to be doneby time 0, before uncertainty resolves, and costs c � s.The second step is postponed to time 1 and costs anadditional s if a unit of the semi-finished product fromthe first step is converted to a final product. The anal-ysis shows how different levels of postponementaffect the firm’s strategic position, which is in somesense similar to Ware (1984).

b

VO

I ( σ

2 )

(a) Firms’ Strategic Choices (s ∈ { −∞, 0, 0.9 })

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14

16

18

20

0

−∞

−∞

0.90

s

s 0.9

E−E

R−R

R−R orE−E

VOCEh

VOCRh

b

VO

I ( σ

2 )

(b) Socially Efficient Strategies (s ∈ { −∞, −1, 0, 0.5, 0.9 })

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14

16

18

20

R−R

E−R

0

−1

−∞

0.9

s0.5

Figure 8 Firms’ Strategic Choices in Equilibrium and Socially Efficient Strategies for the Holdback Model (Arrow Indicates Increasing Salvage Values): (a) Firms’ Strategic Choices (s ∈ {�‘,0,0.9}); (b) Socially Efficient Strategies (s ∈ {�‘,�1,0,0.5,0.9})

−3 −2.5 −2 −1.5 −1 −0.5 0 0.5 12

2.5

3

3.5

4

4.5

5

5.5

6

6.5

7

s

quan

tity

qE

qR

QE

Figure 9 Firms’ Output Quantities as a Function of Salvage Value


4.4. Fixed Cost DifferentialIn addition to the strategic and informational con-cerns studied in the previous analysis, we nowinclude a third concern regarding the cost premiumof responsiveness. Consider the case where respon-siveness requires an additional fixed cost K. Sucha fixed cost can represent an investment in infra-

structure, such as a distribution center in or near theconsumer market, that enables responsiveness. Alter-natively, a firm could provide responsiveness by pay-ing for expedited transport at higher marginal costbut no additional fixed cost. We address this highermarginal cost case in the next section. Figures 10 and11 show firms’ strategic choices and the social

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

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8

10

12

14

16

18

20

b

VO

I (σ2

)


R−R

R−R orE−E

VOCEΔ

VOCRΔ

E−E

E−R

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14

16

18

20

b

VO

I (σ2

)


E−E

E−R

R−R

Figure 10 Firms’ Strategic Choices in Equilibrium and Socially Efficient Strategies with Fixed Cost Differentials (K = 1): (a) Firms’ StrategicChoices; (b) Socially Efficient Strategies

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

2

4

6

8

10

12

14

16

18

20

b

VO

I (σ2

)


E−E

R−R

E−R

VOCEfcVOCRfc

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14

16

18

20

b

VO

I (σ2

)


E−E

E−R

R−R

Figure 11 Firms’ Strategic Choices in Equilibrium and Socially Efficient Strategies with Fixed Cost Differentials (K = 3): (a) Firms’ StrategicChoices; (b) Socially Efficient Strategies


efficient choices for K = 1 and K = 3, respectively. Forconsistency with previous figures, we leave the axesas r2 and b and label the curves separating the strat-egy space as VOCEfc and VOCRfc; although it shouldbe noted that these curves now capture both commit-ment and cost effects of choosing responsiveness.To understand the implications of fixed cost, we

characterize these curves using Equations (17) and(18) from the approximation of the basic model andincorporate the fixed cost of responsiveness K:

pRjE � pEjE ¼ 14½VOI � VOCE� � K;

¼ 14½VOI � ðVOCE þ 4KÞ�;

ð21Þ

pRjR � pEjR ¼ 1ð2þ bÞ2 ½VOI � VOCR� � K;

¼ 1ð2þ bÞ2 ½VOI � ðVOCR þ ð2þ bÞ2KÞ�:

ð22ÞThe sign of the quantity inside the brackets in Equa-

tions (21) and (22) determines whether or not a firm iswilling to bear the fixed cost K to adopt responsive-ness. It is clear that the presence of the fixed cost Kdiscourages the adoption of responsiveness. Tounderstand why an asymmetric equilibrium can nowexist when it cannot in the base model, recall that inthe base model, the value of commitment when thecompetitor is responsive is less than that value ofcommitment when the competitor is efficient(VOCR � VOCE from Lemma 1). So if a firm will pre-fer responsiveness when its competitor is efficient, itmust also prefer responsiveness when its competitor

is responsive. Here, as ð2 þ bÞ2 � 4 for b ≥ 0, thefixed cost acts as a stronger deterrent when the other

firm is already responsive. This creates the possibilityof the asymmetric equilibrium E–R as seen in Figures10 and 11.From the social point of view, choice E–E is never

preferred in previous models when there is no costpremium associated with responsiveness. Now, how-ever, E–E can be the socially efficient strategy whenthe uncertainty is not too high, as it avoids the fixedinvestment in responsiveness. Also, we can see that,by comparing Figures 10 and 11, the social preferenceis shifting from R–R to E–E as the fixed cost increases.

4.5. Variable Cost DifferentialNext, consider the case where responsiveness comesat a variable cost premium cR ¼ c þ D, where D > 0.The analysis becomes more cumbersome because thecompeting firms may have different variable costs. InTable 2, we provide explicit expressions for theexpected production quantities and profits of the twofirms under the three scenarios (again assumingbounded uncertainty). It is straightforward to seefrom there the impact of the D on firms’ profits: theprofit of a responsive firm decreases in D regardlessof the other firm’s choice; the profit of an efficient firmincreases in D if the other firm is responsive.Similar to the case with fixed cost differential, we

can characterize the firms’ equilibrium choices usingVOI, VOCE, VOCR, and D:

pRjE � pEjE ¼ 14½VOI � ðVOCE þWEÞ�;

pRjR � pEjR ¼ 1ð2þ bÞ2 ½VOI � ðVOCR þWRÞ�;

where

It is not difficult to verify that 0\WE \WR forl � c � D > 0, implying that, as with the fixed cost

Table 2. Game Output with Variable Cost Differential and Bounded Uncertainty

I: E–E II: R–RIII: E–R

E R

Expected quantity (q) l�c2þbl�c�D2þb

ð2�bÞðl�cÞþbD2ð2�b2Þ

ð4�2b�b2Þðl�cÞ�ð4�b2ÞD4ð2�b2Þ

Expected profit (p) ðl�cÞ2

ð2þbÞ2ðl�c�DÞ2þr2

ð2þbÞ2ð2�bÞðl�cÞþbD½ �2

8ð2�b2Þð4�2b�b2Þðl�cÞ�ð4�b2ÞD½ �2

16ð2�b2Þ2 þr24

WE ¼ 2ð16� 8b� 8b2 þ 2b3 þ b4Þðl� cÞD� ð16� 8b2 þ b4ÞD2

4ð2� b2Þ2 ;

WR ¼ 2ð16þ 8b� 4b2 � 2b3 � b4Þðl� cÞD� ð16� 12b2 � 4b3 � b4ÞD2

8ð2� b2Þ :


premium setting, the deterrent from the variable costpremium is stronger when the other firm is alreadyresponsive.Figures 12 and 13 numerically illustrate the impact

of variable cost differential on firms’ strategic choicesand the social efficient choices for D = 0.2 andD = 0.5, respectively. Not surprisingly, we find simi-lar patterns as in the fixed cost premium setting: thepresence of the higher variable cost discourages the

adoption of responsiveness, and it is possible to havethe asymmetric equilibrium E–R.

5. Conclusions

We develop a model to investigate the effect ofcompetition on the choice between efficient andresponsive production. The model enriches the frame-work of Fisher (1997) by incorporating another

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

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4

6

8

10

12

14

16

18

20

b

VO

I (σ2

)


E−E

R−R

E−R

VOCRΔ

VOCEΔ

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14

16

18

20

b

VO

I (σ2

)


E−E

E−R

R−R

Figure 13 Firms’ Strategic Choices in Equilibrium and Socially Efficient Strategies with Variable Cost Differentials (D = 0.5): (a) Firms’ StrategicChoices; (b) Socially Efficient Strategies

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14

16

18

20

b

VO

I (σ2

)


E−E

R−R

VOCEfc

VOCRfc

E−R

R−R orE−E

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14

16

18

20

b

VO

I (σ2

)


E−E

E−R

R−R

Figure 12 Firms’ Strategic Choices in Equilibrium and Socially Efficient Strategies with Variable Cost Differentials (D = 0.2): (a) Firms’ StrategicChoices; (b) Socially Efficient Strategies


dimension—competition—and demonstrates how therelative magnitudes of the value of commitment,which is absent in monopoly models studied in theliterature, and the value of market information jointlydetermine the strategic choice.We find that when market uncertainty is not very

high and/or products offered by competing firms arehighly substitutable, the value of early commitmentcan be large enough to offset the informational benefitderived from responsiveness, even when responsive-ness comes at no cost premium. This is our firstinsight: market conditions, both demand volatilityand intensity of competition, play an important rolein the strategic choice of production technologies.Responsive production becomes more attractive asmarket volatility increases and as product competi-tion becomes less intense. A corollary to this firstinsight then is that product innovation (resulting inless competition) is complementary with responsiveproduction, often considered a process innovation.In addition to the basic model, we also considered

some extensions where firms had fewer operationalconstraints and greater operational flexibility. Quitecontrary to our first-order intuition, these so-calledimprovements lead to negative effects on firms’choices in competitive situations. If firms are allowedto decide the timing of their decision, they end updeciding at the very beginning in equilibrium. Ifresponsive firms are allowed to produce freely in bothperiods as opposed to only in the second period, firmsare more likely to choose to be efficient. If efficientfirms are allowed to hold back products producedearlier (a setting which can also be interpreted aspostponed production), firms are more likely tochoose responsive. This suggests the second maininsight: the power of commitment is negativelyrelated to operational flexibility. In competitive situa-tions where commitment plays an important role,firms that are less operationally flexible can takegreater strategic advantage.Our study illustrates how competition can drive the

self-interested firms into a Pareto dominated equilib-rium and lead to loss of social efficiency. One mayexpect that the dilemma will be further aggravated ifthere are more players competing in the game. Inpractice, firms might overcome this issue and realizethe potential profit improvement by committing to beresponsive through the same third party logistics pro-vider or by a powerful retailer mandating supplierresponsiveness.

Acknowledgments

The authors gratefully acknowledge the timely andthoughtful feedback from the department editor, senior edi-tor, and two anonymous referees. The first author’s research

was supported in part by National University of Singaporeacademic research grants R-314-000-076-133 and R-314-000-084-112.

Appendix: ProofsIn this appendix we present proofs and derivationsrelated to the basic model. Proofs for results related tomodel extensions (Proposition 2–6) are available inthe online Supporting Information.

Derivation of Table 1For Scenario I (E-E), the production quantities andprofits are deterministic, which is derived in Equa-tions (6) and (7).For Scenario II (R-R), when the uncertainty about

ξ is bounded such that the probability of ξ � c < 0is negligible, Equations (10) and (11) can be simpli-fied to

qRjR ¼ l� c2þ b ; p

RjR ¼ E n� c2þ b

� �2" #¼ ðl� cÞ

2 þ r2ð2þ bÞ2 :

For Scenario III (E-R), we know for any deter-ministic ξ that is larger than the marginal cost c,Firm 1 always produces the Stackelberg leaderquantity and Firm 2 always enter the market byproducing a positive Stackelberg follower quantity.When the uncertainty about ξ is low, we can expecta positive q2 ¼ n�c�bq12 . The profit of Firm 1 is thenreduced to

p1ðq1Þ ¼ E½ðp1ðq1; q2ðq1; nÞ; nÞ � cÞq1�¼ E n� c� q1 � b

2ðn� c� bq1Þ

� �q1

¼ 2� b2

ðl� cÞq1 � 2� b2

2q21:

So

qEjR1 ¼2� b

2ð2� b2Þ ðl� cÞ; pEjR1 ¼

ð2� bÞ28ð2� b2Þ ðl� cÞ

2:

By Equation (13), Firm 2’s expected productionquantity is

qRjE2 ¼ E½q2ðqEjR1 Þ� ¼ En� c� bqEjR1

2

" #

¼ 4� 2b� b2

4ð2� b2Þ ðl� cÞ;

and its profit

pRjE2 ¼ E ðn� q2ðqEjR1 Þ � bqEjR1 � cÞq2ðqEjR1 Þh i

¼ ð4� 2b� b2Þ2

16ð2� b2Þ2 ðl� cÞ2 þ r

2

4:


PROOF OF LEMMA 1. For 0 ≤ b ≤ 1,

VOCR0 ¼ b

3ð4� b2Þ4ð2� b2Þ2 ðl� cÞ

2�0

VOCE0 ¼ b

2ð�b5þ2b4�6b3�32b2þ8bþ48Þ½ð2� b2Þð2þ bÞ�3 ðl� cÞ

2�0

VOCE

VOCR¼ 2ð�b

3�8b2þ16Þbð�b4�4b3�2b2þ8bþ8Þ �1:

h

PROOF OF PROPOSITION 1. We have three possible cases:

1. If VOI < VOCR, then PRjR \PEjR andPRjE \PEjE. So E is a dominant strategy, inde-pendent of the other firm’s choice.

2. Similarly, if VOI > VOCE, then PRjR [ PEjR

and PRjE [ PEjE. R is a dominant strategy.3. When VOCR ≤ VOI ≤ VOCE, PRjR [PEjR and

PRjE \PEjE, E-E and R-R are the twoNash equilib-ria.

The asymmetric equilibrium E-R would occur ifVOCE ≤ VOI ≤ VOCR. However, since VOCR ≤ VOCE

(by Lemma 1), it will never happen. h

PROOF OF COROLLARY 1. VOI is increasing in r2 whileVOCE and VOCR are independent of r2. Responsive-ness is more favorable when r2 is larger.

When b = 0, the two products are independent andthere is no strategic concern. Choosing R is alwaysbeneficial. Since VOI is independent of b, and VOCE

and VOCR are increasing in b and l, the game out-come will shift from R-R to E-E as b or l increases. h

Derivation of Table 2. For Scenario I (E-E), the pro-duction quantities and profits are not affected by thecost premium and remain the same as in Equations(6) and (7). For Scenario II (R-R), when the uncertaintyabout ξ is bounded such that the probability ofξ�(c+D) < 0 is negligible, the production quantitiesand profits can be similarly derived as for Table 1000if we replace variable cost c by c + D:

qRjR ¼ l� c� D2þ b ;

pRjR ¼ E n� c� D2þ b

� �2" #¼ ðl� cÞ

2 þ r2ð2þ bÞ2 :

For Scenario III (E-R), when the uncertainty about ξis low, we can expect a positive q2 ¼ n�c�D�bq12 . Theprofit of Firm 1 is then reduced to

p1ðq1Þ ¼E ðp1ðq1; q2ðq1; nÞ; nÞ � cÞq1½ �

¼E n� c� q1 � b2ðn� c� D� bq1Þ

� �q1

¼ 2� b2

ðl� cÞq1 þ bD2q1 � 2� b

2

2q21:

So

qEjR1 ¼ð2� bÞðl� cÞ þ bD

2ð2� b2Þ ;

pEjR1 ¼½ð2� bÞðl� cÞ þ bD�2

8ð2� b2Þ :

Firm 2’s expected production quantity is

qRjE2 ¼ E q2ðqEjR1 Þh i

¼ E n� c� D� bqEjR1

2

" #

¼ ð4� 2b� b2Þðl� cÞ � ð4� b2ÞD4ð2� b2Þ ;

and its profit

pRjE2 ¼ E ðn� q2ðqEjR1 Þ � bqEjR1 � cÞq2ðqEjR1 Þh i

¼ ½ð4� 2b� b2Þðl� cÞ � ð4� b2ÞD�216ð2� b2Þ2 þ

r2

4:

ReferencesAnand, K. S., K. Girotra. 2007. The strategic perils of delayed dif-

ferentiation. Manage. Sci. 53(5): 697–712.

Cachon, G., G. Kök. 2010. Competing manufacturers in a retailsupply chain: On contractual form and coordination. Manage.Sci. 56(3): 571–589.

Caro, F., V. M. de Albeniz. 2010. The impact of quick response ininventory-based competition. Manuf. Serv. Oper. Manag. 12(3):409–429.

Christen, M., W. Boulding, R. Staelin. 2009. Optimal market intel-ligence strategy when management attention is scarce. Man-age. Sci. 55(4): 526–538.

Fisher, M., J. Hammond, W. Obermeyer, A. Raman. 1997. Config-uring a supply chain to reduce the cost of demand uncer-tainty. Prod. Oper. Manag. 6(3): 211–225.

Fisher, M., A. Raman. 1996. Reducing the cost of demanduncertainty through accurate response to early sales. Oper.Res. 44(1): 87–99.

Fisher, M. L. 1997. What is the right supply chain for your prod-uct? Harv. Bus. Rev. 75(2): 105–116.

Gerwin, D. 1993. Manufacturing flexibility: A strategic perspec-tive. Manage. Sci. 39(4): 395–410.

Goyal, M., S. Netessine. 2007. Strategic technology choice andcapacity investment under uncertainty. Manage. Sci. 53(2):192–207.

Iyer, A., M. Bergen. 1997. Quick response in manufacturer-retailerchannels. Manage. Sci. 43(4): 559–570.

Krishnan, H., R. Kapuscinski, D. A. Butz. 2010. Quick responseand retailer effort. Manage. Sci. 56(6): 962–977.

Lee, H. 2002. Aligning supply chain strategies with productuncertainties. Calif. Manag. Rev. 44 (3): 105–119.


Lin, Y.-T., A. Parlakt€urk. 2012. Quick response under competition.Prod. Oper. Manag. 21(3): 518–533.

Maggi, G. 1996. Endogenous leadership in a new market. RANDJ. Econ. 27(4): 641–659.

McGuire, T. W., R. Staelin. 1983. An industry equilibrium analy-sis of downstream vertical integration. Mark. Sci. 2(2): 161–191.

Pal, D. 1991. Cournot duopoly with two production periods andcost differentials. J. Econ. Theory 55: 441–448.

Randall, T., K. Ulrich. 2001. Product variety, supply chain struc-ture, and firm performance: Analysis of the US bicycle indus-try. Manage. Sci. 47(12): 1588–1604.

Randall, T. R., R. M. Morgan, A. R. Morton. 2003. Efficientversus responsive supply chain choice: An empirical exami-nation of influential factors. J. Prod. Innov. Manag. 20(6): 430–443.

Ray, S., S. Li, Y. Song. 2005. Tailored supply chain decision mak-ing under price-sensitive stochastic demand and deliveryuncertainty. Manage. Sci. 51(12): 1873–1891.

Saloner, G. 1987. Cournot duopoly with two production periods.J. Econ. Theory 42(1): 183–187.

Singh, N., X. Vives. 1984. Price and quantity competition in adifferentiated duopoly. RAND J. Econ. 15(4): 546–554.

Van Mieghem, J. A., M. Dada. 1999. Price versus production post-ponement: Capacity and competition. Manage. Sci. 45(12):1631–1649.

Vives, X. 2000. Oligopoly Pricing: Old Ideas and New Tools. MITPress, Cambridge, MA.

Wang, T., A. Atasu, M. Kurtulus. 2012a. A multiordering news-vendor model with dynamic forecast evolution. Manuf. Serv.Oper. Manag. 14(3): 472–484.

Wang, Y., B. Niu, P. Guo. 2012b. On the advantage of quantityleadership when outsourcing production to a competitivecontract manufacturer. Prod. Oper. Manag. 22(1): 104–119.

Ware, R. 1984. Sunk costs and strategic commitment: A proposedthree-stage equilibrium. Econ. J. 94: 370–378.

Wharton, T. J., E. M. White. 1988. Flexibility and automation: Pat-terns of evolution. Oper. Manag. Rev. 6(3 & 4): 1–8.

Wu, X., F. Zhang. 2013. Home or overseas? An analysis of sourcingstrategies under competition. SSRN. Available at http://ssrn.com/abstract=1871425 or http://dx.doi.org/10.2139/ssrn.1871425 (accessed date July 7, 2013).

Zhao, X. 2008. Coordinating a supply chain system with retailersunder both price and inventory competition. Prod. Oper.Manag. 17(5): 532–542.

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Appendix: proofs.


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