strategic decisions of new technology adoption under...

Decision SciencesVolume 34 Number 4Fall 2003Printed in the U.S.A.

Strategic Decisions of New TechnologyAdoption under Asymmetric Information:A Game-Theoretic Model∗

Kevin Zhu†

Graduate School of Management, University of California, Irvine, CA 92697-3125,e-mail: [email protected]

John P. WeyantRoom 446, Terman Building, Department of Management Science and Engineering,Stanford University, Stanford, CA 94305-4026, e-mail: [email protected]

ABSTRACT

In this paper we explore strategic decision making in new technology adoption by usingeconomic analysis. We show how asymmetric information affects firms’ decisions toadopt the technology. We do so in a two-stage game-theoretic model where the first-stage investment results in the acquisition of a new technology that, in the second stage,may give the firm a competitive advantage in the product market. We compare two in-formation structures under which two competing firms have asymmetric informationabout the future performance (i.e., postadoption costs) of the new technology. We findthat equilibrium strategies under asymmetric information are quite different from thoseunder symmetric information. Information asymmetry leads to different incentives andstrategic behaviors in the technology adoption game. In contrast to conventional wis-dom, our model shows that market uncertainty may actually induce firms to act moreaggressively under certain conditions. We also show that having better information is notalways a good thing. These results illustrate a key departure from established decisiontheory.

Subject Areas: Asymmetric Information, Information Economics, Strate-gic Decisions, Technology Adoption, and Technology-Based Competition;Functional Areas: Information Technology, Interorganizational Systems,and Strategic Information Systems; and Methodological Areas: EconomicAnalysis and Game Theory.

∗We are grateful to Robert Wilson, William Sharpe, Haim Mendelson, Hau Lee, James Sweeney, andBlake Johnson for valuable suggestions on our initial work of this research at Stanford University. Wesubsequently received constructive comments from Vijay Gurbaxani, Rajeev Tyagi, Sajeev Dewan, BarrieNault, Robin Keller, Eric Clemons, David Croson, and Tridas Mukhopadhyay, which are greatly appreciated.The first author also wishes to thank seminar participants at Stanford, Wharton, CMU, UCLA, UC Irvine,the INFORMS and the WISE conferences, for valuable comments. The usual disclaimer applies.

†Corresponding author.

643

644 Strategic Decisions of New Technology Adoption

INTRODUCTION

In recent years, rapid technological progress, especially in information and com-puter technologies, has heightened the strategic importance of new technologies ina competitive marketplace (Porter & Millar, 1985). In today’s technology-driveneconomy, new innovations develop rapidly, and managers constantly face adoptiondecisions. Companies often invest in new technologies in the hope to gain an edgeover their competitors (Clemons, 1991; Parsons, 1984). A survey shows that 50%of technology executives indicated that to “gain competitive advantage” was the toppriority that influenced their organization’s increase in Internet-based technologyinvestment, and 21% believed that “responding to a competitor” was also a keyfactor (Goldman Sachs, 2000).

In an oligopolistic industry, one firm’s technology adoption decision couldaffect the market structure and strategic equilibrium. While the tangible value (e.g.,improvement in productivity and operational efficiency) of new technologies hasbeen the focus of the literature, a few recent studies show that a major driverof investment in technology lies in the strategic value gained from altering thecompetitive equilibrium (e.g., Barua & Lee, 1997; Dewan & Mendelson, 1998;Wang & Seidmann, 1995; Riggins, Kriebel, & Mukhopadhyay, 1994; and Zhu,1999).

New technologies in our study may refer to any technologies that are criticalto the firm’s ability to compete in the product market. Our model will abstractaway from specific technologies, though information technologies seem to exhibitthese features more often than traditional technologies. Their deployment oftenhelps the company to reduce cost or serve new markets (Kathuria, Anandarajan, &Igbaria, 1999). For example, auto manufacturers, such as Ford and General Motors(GM), invested heavily in electronic data interchange (EDI) and, more recently,in business-to-business (B2B) e-procurement systems to reduce costs and, hence,gain a competitive edge over their rivals in the auto market. Similarly, Dell andGateway are leveraging their investments in Internet-based supply chain systemsto gain advantages over competitors. In addition to these examples, successfulstrategic applications of new technology in achieving competitive gains are abun-dantly documented in the literature, including American Airline’s SABRE com-puter reservation system, Wal-Mart’s inventory information system, and FedEx’spackage tracking system (Clemons, 1991). A common benefit of these adoptions isthe capability to compete in product markets at lower cost or with better efficiency.In some situations, without the new technology, the firms would not be able tocompete in the market.

These examples also illustrate that technology adoption decisions are of-ten made under strategic considerations or competitive pressure. Indeed, in anoligopolistic industry with several competitors, adopting a new technology is astrategic decision. On the one hand, facing uncertainty about the new technology,each firm has an incentive to delay the adoption decision until it receives moreinformation to resolve uncertainties about the new technology’s cost and perfor-mance. On the other hand, if it does so, it runs the risk that another firm maypreempt it by adopting first because technological investments often exhibit earlymover advantages due to standard-setting, economies of scale, brand recognition,

Zhu and Weyant 645

and other factors (Katz & Shapiro, 1986; Dasgupta, 1986). Fear of preemption bya rival creates incentives to act quickly. This dilemma is especially important whenthe market is volatile and the future performance of the new technology is uncer-tain. Thus, the tradeoff between adopting early and waiting for more informationelevates the strategic importance of leader-follower dynamics.

What makes these decision dynamics more complicated, yet more interest-ing, is information asymmetry across firms. Information asymmetry arises whenone firm has more information than others. This may be due to factors such asprior investment in related technologies (the learning effect), information-gatheringactivities, or in-house knowledge about the implementation process. Real-worldobservation has provided us with many situations in which companies are indeedasymmetrically informed. For example, Dell Computer may have better informa-tion on the cost structure of the “build-to-order” model than traditional PC makerssuch as IBM and Compaq (now Hewlett-Packard [HP]). A firm such as Ford thathas experienced similar technologies (e.g., EDI) may know more about the costfunctions of Internet-based e-procurement technologies than a firm without suchexperience. The existence of information asymmetry may have significant effectson technology adoption decisions in an oligopolistic industry, although it is unclearwhat exactly these effects may be.

The following scenario may help illustrate the strategic decision-setting. As-sume that an industry consists of two manufacturers, A and B. They both attemptto invest in a new computerized technology that will enable them to produce anew product and serve a new market segment. However, their technology-adoptionefforts may involve technical uncertainty in the sense that implementation of thenew technology may or may not achieve the expected performance. In other words,postadoption costs may be low, if the implementation succeeds, or high, if it fails.Due to prior experience with related technologies or in-house knowledge aboutthe implementation process, one firm (say, firm A) has superior information aboutthe true cost function associated with the new technology. That is, firm A knowssomething that firm B does not know. Hence, information is asymmetric acrossthese two firms.

Motivated by these kinds of strategic considerations, we study the link be-tween technology adoption decisions and the information structure under whichthe decisions are being made. Our research questions are: (1) What happens tothe adoption decisions if firms have asymmetric information regarding the futureperformance of a new technology? (2) Under what conditions will firms adopt thetechnology early, and under what conditions will they wait and allow their competi-tor to become a leader? (3) What is the effect of market uncertainty on the adoptionpattern? and (4) Is having more information always a good thing in technologyadoption games?

To better understand these issues, we build a simple model with stylizedparameters, where asymmetric information arises from the future performance (i.e.,postadoption costs) of the new technology. We use a game-theoretic perspective,which enables us to examine the strategic responses of competing firms. We focuson a two-stage adoption game between two competing firms. First they investin capability in the first stage, and then optimally exploit the capability in thesecond stage, contingent on the technology having been implemented. Naturally,


the first-stage adoption can influence the firm’s strategic position in the second-stage competition in the downstream product market.

Either firm can make a preemptive move (as a Stackelberg leader), but thisearly move may reveal its private information about the new technology to its rival.Conversely, a firm may choose to wait (as a Stackelberg follower) in order to learnfrom the other firm’s adoption decisions. In this setting, the better-informed firmlearns less from the other firm’s actions, and often chooses to move first, even whenit suffers cost disadvantage. The less-informed firm may actually prefer to be a fol-lower, willing to sacrifice the early-mover advantage, since the benefits of learningfrom the leader’s actions may outweigh the costs of “Stackelberg followership.”Thus, a leader-follower dynamic may be induced endogenously by the informationasymmetry.

Relationship to the Literature

Our study is related to several streams of literature in technology adoption, researchand development (R&D) innovations, economics, and information technology. Thegame-theoretic literature on technological competition has demonstrated that theadoption of a new technology often exhibits a preemptive feature—each firm tries topreempt its rivals by investing early (Fudenberg & Tirole, 1985; Katz & Shapiro,1986; Dasgupta & Stiglitz, 1980; Reinganum, 1985; and Spence, 1985). Whilestressing the preemptive effects of early commitment on deterring entrants or en-hancing market share, this literature does not emphasize the role of uncertainty,which may tend to smooth out the incentive to move early (Dixit & Pindyck, 1994).

In modeling technology adoption decisions it might be helpful to consider areal options perspective, viewing investment projects as real options. The oppor-tunity to adopt a new technology is equivalent to a call option with an exerciseprice equal to the investment outlay, and the underlying asset is the new tech-nology. Several studies view technology investments as real options, includingKambil, Henderson, and Mohsenzadeh (1993), Benaroch and Kauffman (1999),Zhu (1999), and Tallon, Kauffman, Lucas, Whinston, and Zhu (2002). These stud-ies documented the crucial role of flexibility in investment decisions under un-certainty. Yet the real options literature has been typically based on two specificassumptions: (a) the firm has a monopoly power over an investment opportunity,and (b) the product market is perfectly competitive. As a result, investment doesnot affect product market competition. In contrast to the technological competitionliterature that focuses on preemption, the real options literature stresses the optionvalue to wait, but ignores the risk of competitive preemption.

In the adoption literature related to information technologies, several studiesfocus on the possibility of gaining a competitive advantage via the impact onmarket structure of interorganizational systems (IOS). Among others, Barua andLee (1997), Riggins et al. (1994), and Wang and Seidmann (1995) studied EDIadoption strategies and competitive effects. They analyzed the introduction of EDIin a vertical market involving a single manufacturer and several suppliers, wherethe manufacturer faces a linear demand curve and the competing suppliers haveupward-sloping marginal cost functions. They demonstrated that a supplier mighthave to join the EDI network out of competitive pressure or “strategic necessity.”

Zhu and Weyant 647

These papers substantially improved our understanding about strategic de-cision making in technology adoption. Yet, a common assumption made in theliterature is symmetric information. That is, firms have symmetric information setsand no private information is involved. We build on these studies, particularly thegame-theoretic modeling of IOS, and address additional concerns arising frominformation asymmetry, an issue on which the literature has not yet focused. Aswe shall see, information asymmetry leads to different incentives and strategic be-haviors in the technology adoption game. By relaxing the typical full-informationassumption in the literature, our model allows us to gauge the effect of informa-tion asymmetry on technology adoption decisions and to show how asymmetricinformation alters the adoption equilibrium.

The remainder of this paper proceeds as follows. The next section describesthe basic setup of the model. The third section derives the subgame equilibriumquantities and adoption decisions under asymmetric information. The fourth sec-tion explores the effects of information asymmetry on adoption decisions where,we show that, having better information is not necessarily better. A final sectionconcludes the paper. We emphasize the results in the text and relegate the technicalproofs to the appendices. For readers’ convenience, a list of notations is summarizedat the end of the paper.

THE MODEL SETUP

In this section, we construct a two-stage game-theoretic model. We try to keepthe model simple so that we can focus on the key issues identified above. In aduopoly industry that consists of two companies, competition proceeds in twoconstituent stages: first, the adoption (or investment) stage and then the production(or market) stage, as shown in Figure 1. A firm adopts, in the first stage, the

Figure 1: The two-stage technology adoption game.

ProductMarket

qA

qB

Tech

Tech

{I, D}

cA

cB

{I, D}Firm A

Firm B ( , , ) ( )i i j i jP q q b q qΘ = Θ− +

Adoption stage Production stage

I II

ProductMarket

qA

qB

Tech

Tech

{I, D}

cA

cB

{I, D}Firm A

Firm B ( , , ) ( )i i j i jP q q b q qΘ = Θ− +

Adoption stage Production stageAdoption stage Production stage

I II

Firms A and B decide whether to invest or defer, {I, D}, in a new technology at the first stage.Production quantity decisions, qi , follow in the second stage, where the two firms competein the same product market. Revenues are realized according to the resulting Nash-Cournotequilibrium.


new technology that will enable the firm to produce a product and serve a newmarket in the second stage. The strategic impact of technology adoption in thefirst stage is captured through its impact on competitive reactions and equilibriumpayoffs.

More formally, we define the technology adoption game as follows:

Players: Firm A and firm B.

Sequence of events: (i) adopt the technology, (ii) decide how much to produce,(iii) compete in the product market.

Strategies: At the adoption stage, each firm decides to invest immediately (I),defer to the next period (D), not invest at all (N) in an indivisible technologythat requires a lumpy investment outlay, I. If a firm decides to adopt thetechnology, it also needs to decide, at the second stage, how many units ofthe product to produce, that is, a quantity qi that maximizes its expectedpayoff.

Payoffs: The payoff to firm i is a function of the strategies chosen by it and itscompetitor. If both firms make decisions simultaneously (without observingeach other), they will split the market according to a Nash-Cournot equilib-rium. If one firm adopts first and the other does later, their payoffs will bedetermined through a Stackelberg equilibrium (Fudenberg & Tirole, 1991).Figure 2 illustrates these possible combinations.

Note that the game has two stages; and each stage has multiple periods. The in-vestment stage lasts for two periods and the adoption game ends after the secondperiod or when both firms have invested, whichever happens first. The technology,once installed, continues to generate cash flows for n periods in the productionstage. During the investment stage, a firm can choose to invest in the first period(I), defer to the second period and invest then (D), or not invest at all during thesetwo periods (N), which means the firm drops out of the market with no capabilityto compete in the market stage.

Figure 2: The game tree.

B

I

D

A

I

D

I

D

A

Outcome Payoffs

(I, I)

(I, D)

(D, I)

(D, D)

,NS NSA BV V

,SF SLA BV V

,SL SFA BV V

2 2,NS NSA BV V

BB

I

D

AA

I

D

I

D

AA

Outcome Payoffs

(I, I)

(I, D)

(D, I)

(D, D)

,NS NSA BV V

,SF SLA BV V

,SL SFA BV V

2 2,NS NSA BV V

This shows the four possible combinations of the adoption strategies, (I, I), (I, D), (D, I),and (D, D), as well as the corresponding payoffs. For example, if both firms invest (I, I),they receive payoffs V N S

A and V N SB respectively, where the subscripts denote the firms and

superscripts represent the paths.

Zhu and Weyant 649

To keep it simple, we assume that market demand is linear and can be repre-sented by the following inverse demand function,

P(�, qi , q j ) = � − b(qi + q j ), b > 0, i, j = A, B, i �= j (1)

where P is the price of the product; qi and qj are the quantities of products suppliedby firms i and j respectively; b is a constant representing demand elasticity; � isthe demand intercept. We will consider two situations: constant demand � firstand stochastic demand �̃ in later sections.

A firm’s cost function is determined by its technology. The cost function forfirm i is defined by

Ci (qi ) = ci qi , (2)

where Ci is the total cost, and ci is the marginal cost of firm i (I = A, B). Inaddition to the production cost, firms need to incur a lumpy investment outlay, I,in order to acquire the new technology. To avoid incentives from possible changeof investment cost, we assume that the investment outlay grows at the same rate asthe discount rate, that is,

I2 = (1 + r )I1. (3)

where r is the discount rate and I i is the investment outlay in period i.

Model of Asymmetric Information

Recognizing that there are many possible ways that asymmetric information mayarise, we abstract from other possibilities and focus on asymmetric informationabout cost so that we can isolate the role of asymmetric information in technologyadoption decisions. In terms of modeling, cost seems a reasonable place to start,and the result from this model would help building more complicated models.Also, the focus on cost has some empirical support (Mukhopadhyay, Kekre, &Kalathur, 1995). Furthermore, we believe that cost benefit is fairly general to theextent that other benefits can be translated into equivalent cost impacts (i.e., betterquality or service can be translated into lower cost in the sense that a firm needsto equalize the same level of quality or service at some extra cost). Therefore,analogous results could be obtained if the investment results in greater productquality or better customer service. See Spence (1985) for an analytical formulationof this view.

Specifically, the asymmetric information is defined as follows:

(i) Firm A has full information on both firms’ cost functions (status quo inliterature).

(ii) Firm B knows its own cost function, cB, but has incomplete informationabout firm A’s cost function. Firm B depicts this incomplete informationby the following probability distribution:

EB(cA) ={

cH with probability ξ

cL with probability (1 − ξ )(4)

where cL < cB ≤ cH to avoid trivial cost advantage. To firm B, cA

is a stochastic variable with mean, EB(cA) = ξcH + (1 − ξ )cL, and


variance, σ 2c . As we can see, probability ξ is essentially a measure of

firm B’s belief, which represents a standard Bayesian assessment of thechance that the competitor’s cost is high.

(iii) The parameters ξ , cH , cL, and cB are common knowledge, while firmA’s true cost cA is private information known to firm A only. That is,their information sets are ISA = {cA, cB, �} and ISB = {cL, cH , ξ ,cB, �}, respectively.

In this model, firm A has better information than firm B about the postadoptioncost, thus information is asymmetric. The asymmetry is captured by ξ and σ 2

c .This simple model is a modest departure from the literature where both firms hadsymmetric information.

ANALYSIS OF ADOPTION DECISIONS

To analyze the two-stage game, we first need to derive the subgame equilibriumquantities and payoffs for the second stage, assuming that the technology has beenput in place in the first stage. We then use these results to analyze the technology-adoption decisions in the first stage. This approach is the backward inductionsolution method well known in game theory (Fudenberg & Tirole, 1991). We nowfocus on the second-stage subgame equilibrium quantities and profits.

Optimal Quantities and Equilibrium Profits

There are two possible situations in the second-stage competition: simultaneousand sequential moves.

Simultaneous moves

Firms A and B simultaneously decide the quantity of product to produce. Sincefirm A knows its own cost function, it will choose a quantity, conditional on its truecost, that maximizes its expected profit. Naturally, firm A may want to choose alower quantity if its marginal cost is high than if it is low. Firm B, for its part, shouldanticipate that firm A will tailor its quantity to its costs in this way. However, firmB has only a probability distribution on firm A’s cost. It has to optimize its profitunder this incomplete information. Let q∗

A(cH) and q∗A(cL) denote firm A’s optimal

quantities as a function of its costs, and q∗B denote firm B’s single optimal quantity.

The following optimal quantities are derived in Appendix A:{q∗

A = 13b

[� − 1

2 (3cA − 2cB + EB(cA))]

q∗B = 1

3b [� − 2cB + EB(cA)](5)

The corresponding equilibrium profits are, respectively,{π∗

A = 19b

[� − 1

2 (3cA − 2cB + EB(cA))]2

π∗B = 1

9b [� − 2cB + EB(cA)]2(6)

The equilibrium quantities essentially represent the intersection of the two firms’best response functions. Its solution requires information about market demand,the firm’s own cost and estimate about the rival’s cost, all of which are known

Zhu and Weyant 651

parameters in their information sets. Firm i’s quantity (and profit) will be higher ifits own cost is lower or rival’s cost is higher. Equation (5) can be written as

q∗

A(cH ) = 13b (� − 2cH + cB) + 1 − ξ

6b (cH − cL )

q∗A(cL ) = 1

3b (� − 2cL + cB) − ξ

6b (cH − cL )

q∗B = 1

3b [� − 2cB + ξcH + (1 − ξ )cL ]

Compare the equilibrium quantities q∗A(cH), q∗

A(cL), and q∗B here to the Nash-

Cournot equilibrium under full information where firm i would produce q∗i =

13b (� − 2ci + c j ) (Varian, 1992, p. 285–291). Under asymmetric information,q∗

A(cH) is greater than 13b (� − 2cH + cB) and q∗

A(cL) is less than 13b (� − 2cL + cB).

This occurs because both firms not only tailor their production decisions to theirown costs but also respond to the competitor’s adjustments resulting from the in-formation asymmetry. This illustrates that strategic interactions affect productiondecisions, where not only a firm’s own cost parameter but also the competitor’scost parameter enter their decisions as shown in (5).

The profits in (6) represent the cash flows generated by the new technologyin each production period. Recall that the discount rate is r, the present value ofinvesting in the technology can be calculated by summing up the profit of the initialperiod and the discounted cash flows of all future periods, minus the investmentoutlay: {

V N SA = 1 + r

9br

[� − 1

2 (3cA − 2cB + EB(cA))]2 − I

V N SB = 1 + r

9rb [� − 2cB + EB(cA)]2 − I(7)

where VNSi represents the present value of firm i under Nash-Cournot equilibrium

(NS).

Sequential moves

Under asymmetric information, the order of sequential moves may reveal privateinformation. Firms can infer information by observing other firms’ actions. Thesequencing of moves becomes subtler, as it reflects each firm’s calculated tradeoffbetween the early mover advantage and the informational benefit of waiting to learnrival’s private information (i.e., information revelation). We allow the sequencingto be endogenously determined through firms’ profit-optimizing decisions, undertwo possible sequences.

(a) The less-informed firm (B) moves first and the more-informed firm (A) follows.Similar to the above approach, the optimal quantities are derived in Appendix Aas: {

q SF∗A = 1

4b [� − 2cA + 2cB − EB(cA)]

q SL∗B = 1

2b [� − 2cB + EB(cA)](8)

The corresponding equilibrium net present values can be derived as follows:{V SF

A = 116rb [� − 2cA + 2cB − EB(cA)]2 − I

V SLB = 1

4b (� − cB)2 + 18rb [� − 2cB + EB(cA)]2 − I

(9)


where VSLi and VSF

i represent the value for the Stackelberg leader (SL) andStackelberg follower (SF), respectively. The results in and constitute a BayesianNash equilibrium, because each firm’s choice is the best response to the otherfirm’s decisions, given its belief about its competitor’s cost functions (Fudenberg& Tirole, 1991).

(b) The more-informed firm (A) moves first and the less-informed firm (B) follows.If the firm with private information moves first, the follower would have an op-portunity to infer the leader’s private information through revealed actions. Morespecifically, firm B would observe firm A’s quantity decisions, q∗

A(cH) or q∗A(cL),

and infer firm A’s costs, cH or cL, correspondingly. This relationship is based onthe revelation principle from economics (Tirole, 1988). Since q and c are related(i.e., a higher q is associated with a lower c), information about q can be used toestimate c. As a consequence, the impact of the information asymmetry may bemitigated. In our study, we assume that firms make quantity decisions in order tomaximize their expected profits, rather than to mislead competitors. On the otherhand, it is possible that firms may have incentives to signal “low cost” even whentheir true costs are high. Signaling sometimes does happen, but this is limited, atleast to some degree, by the availability of objective information (e.g., financialstatements). Further complications of signaling are out of the scope of this model.See Cho and Kreps (1987) and Fudenberg and Tirole (1991) for discussions ofsignaling games.

Upon observing firm A’s quantity and inferring its private information, firmB chooses its own quantity to maximize its expected profit. The net present valuesat equilibrium are derived in Appendix A as follows:{

V SLA = 1

4b (� − cA)2 + 18rb (� − 2cA + cB)2 − I

V SFB = 1

16rb (� − 3cB + 2cA)2 − I(10)

where it is clear that the Stackelberg leader makes greater profit than the follower.

Equilibrium Analysis of Adoption Decisions

Having studied the subgame equilibria in the production stage, we now use theseresults to analyze the technology adoption decisions in the first stage. Both firmsA and B are considering whether to adopt the new technology in anticipation ofthe equilibrium behavior (production quantities derived above) in the second stage.We show the equilibrium conditions under which the firms will invest (I) or defer(D). A strategy pair (firm A’s action, firm B’s action) represents the combinationof firms’ strategies. Namely, (I, D) means that firm A invests and firm B defers. Ofparticular interest are the leader-follower sequences under which firms adopt thenew technology.

For ease of analysis, the whole demand spectrum is divided into four regions.In the first region, the demand is so high that each firm would be able to make aprofit even though they have to split the market. Thus, everyone invests, resulting inthe (I, I) equilibrium. In the second region, firm B cannot be profitable if both firmsinvest. Thus firm B will wait and allow firm A to invest first and become the leader,resulting an (I, D) equilibrium. In the third region, demand is low and both firms

Zhu and Weyant 653

defer to invest in the second period, resulting in a (D, D) equilibrium. If demand isfurther lower such that the market may accommodate only one firm, then if bothinvest, they will end up losing, but either one of them is profitable if only one firminvests and stays in the market. There are two Nash equilibria in this scenario, (I,N) and (N, I), depending on their relative costs, where N means “Not invest.” Thisresult is summarized below, and its derivation is provided in Appendix B.

Proposition 1 (Adoption equilibria under asymmetric information): Under asym-metric information and within a moderate range of market demand, a sequentialpattern (I, D) will emerge where firm A will be the leader while firm B will be thefollower. When market demand is high enough, both firms A and B will adopt thetechnology simultaneously, leading to an (I, I) equilibrium; conversely both willdefer if the market demand is low. That is, the technology adoption game has fourequilibria:

(I, I), if demand is sufficiently high, � ≥ �̄H ;(I, D), if demand is moderate, �̄L ≤ � < �̄H ;(D, D), if demand is low, �̄L2 ≤ � < �̄L and cA = cH;(I, N) or (N, I), if demand is further lower, �̄min ≤ � < �̄L2;(N, N), if demand is extremely low, � < �̄MONO

min , market becomes inactive.

where the thresholds, �̄H , �̄L , �̄L2, �̄min, and �̄MONOmin in descending order, are

derived in Appendix B. In particular,

�̄H = max

{1

2[3cA − 2cB + EB(cA)] + 3

√rbI

1 + r, 2cB

−EB(cA) + 3

√rbI

1 + r, �̄2

}. (11)

In the middle region, the equilibrium is (I, D). That is, the more informed firm(A) invests and the less informed firm (B) defers. This indicates the sequence atequilibrium for who will be the leader and who will be the follower in adoptingthe new technology. The sequential pattern here conveys clear strategic advantage,as the Stackelberg leader makes greater profit than the follower. To see if theseconditions hold with reasonable parameter values, we simulated them under variouscombinations of the parameters and found these conditions can hold true withreasonable parameter values.

The intuition for these equilibria lies in the understanding that firms need tobalance the tradeoff between the payoff benefits of being a leader and the informa-tional benefits of being a follower (i.e., competing for leadership versus waitingfor information). When the demand is high enough, it becomes clear that the pay-off benefits from investing immediately will outweigh any informational benefitsfrom waiting; so both firms invest. In contrast, if the demand is so low that even theextra reward of being a leader cannot compensate for the investment cost requiredto adopt the technology, then both will defer. In the second region, however, thetradeoff is subtler. Firm A captures more profits by being the leader. On the otherhand, firm B, having inferior information, would benefit by waiting and learningthe leader’s (superior) private information. For firm B, the informational benefits


of being a follower outweigh the payoff benefit of being a leader. Therefore, (I, D)can be sustainable as an equilibrium in the second region.

An additional incentive for this (I, D) equilibrium is related to the cost struc-ture. A low-cost firm A (i.e., cA = cL) would always want to invest. A high-cost firmA (i.e., cA = cH) would defer its investment if demand is low. This result leads toa separating equilibrium in the sense that firm A defers only when it is a high-costfirm. Firm B can infer firm A’s high cost by observing the fact that firm A defers.By deferring, firm A would get lower profit than being a Stackelberg leader but stillcannot hide its cost. Knowing this tradeoff, firm A would invest in the first period(as long as demand is above a certain threshold). Consequently, we have:

Corollary 1

The separating equilibrium would not allow firm A to hide its cost by deferring asthis action itself would reveal information to its competitor.

Before we end this section, it might be useful to examine a special case.Assume firm B’s cost equals firm A’s cost (on expectation), that is, EB(cA) = cB,cost asymmetry disappears and only information asymmetry remains between thetwo firms. From (B7) in Appendix B,

E(V N S

B

) − E(V SF

B

) =(

1

9b+ 7

144br

)(� − cB)2 − 1

4brσ 2

c . (12)

It shows that if � is sufficiently large or σ 2c is sufficiently small, firm B should

invest in the first period, leading to an (I, I) equilibrium. On the other hand, if σ 2c

is sufficiently large or � is sufficiently small, firm B should defer the investment,leading to an (I, D) equilibrium. In this case, the (I, D) equilibrium is caused byinformation asymmetry rather than cost asymmetry. In this case, informationaladvantage may transfer to strategic leadership, even without any other advantages.

We may use σ 2c to represent the degree of information asymmetry, whereas

smaller variance means less asymmetry of information. Then, lower variance makesfirm B to be more likely to invest in the first period. The key point is that, when in-formation asymmetry is not severe, it is less useful for firm B to defer the investmentin order to learn firm A’s cost.

The Effect of Demand Uncertainty

In the above section, we assumed that market demand � was constant. Now werelax this assumption by allowing � to change during the first and the secondperiod. The demand is modeled as a simple stochastic binomial variable. Moreprecisely, the demand starts with � in the first period and could move up to u�

with probability p or down to d� with probability 1 − p in the second period,where u and d are the multiplicative parameters of a binomial process (u > 1 andd < 1), as illustrated in Figure 3. We use �̃ to represent the stochastic demandwith expected value, E�̃, and variance, var(�̃) = σ 2

�. Both can be computed fromknown parameters, �, u, d, and p. To keep the model simple, we assume that thedemand stays at either u� or d� beyond the second period so that future cashflows generated by the new technology can be reasonably computed.

Zhu and Weyant 655

Figure 3: Demand uncertainty.

up

Θ

u Θ

d Θ

Pe

p

1-p

up

down

Θ

u Θ

d Θ

Period 1 Period 2

p

1-p

As shown in Appendix C, the net present value expressions in (C1)∼(C4) con-tain extra terms associated with σ 2

�, namely, 1 + r9rb σ 2

�, 116rb σ 2

�, 18rb σ 2

�, and 19rb σ 2

�. No-tice that these extra σ 2

� terms are due to the stochastic nature of the demand. If we setσ 2

� = 0, we return to the case discussed in the previous section. It can be shown thatthe results in the previous section still holds. Thus the introduction of stochastic de-mand does not qualitatively alter the firms’ strategies. Moreover, because of the rel-ative strength of the extra σ 2

� terms, that is, 1 + r9rb σ 2

� > 116rb σ 2

� and 18rb σ 2

� > 19rb σ 2

�,it reinforces the incentives for firm A to invest early. Thus, compared to the case ofconstant demand, firm A has an even stronger incentive to invest in the first period.

For firm B, it can be shown

V N SB − V SF

B = 1

9b[� − 2cB + EB(cA)]2

+ 1

144rb[7E�̃ − 17cB + 10EB(cA)][E�̃ + cB − 2EB(cA)]

+ 7

144rbσ 2

� − 1

4rbσ 2

c

All other terms are positive, hence its sign depends on the sign of

= 7

144rbσ 2

� − 1

4rbσ 2

c , (13)

where two variance terms, var(cA) = σ 2c and var(�̃) = σ 2

� account for the ef-fects of the two stochastic variables, because the model now has two types ofuncertainties—demand uncertainty and cost uncertainty. This suggests that whetherthe equilibrium is (I, I) or (I, D) is determined by the relative degree of demanduncertainty and cost uncertainty. The former works to the advantage to firm B (asit deters its rival from being aggressive), but the latter works as the informationaldisadvantage to firm B.

Severe information asymmetry, as represented by − 14rb σ 2

c , may offset thepositive terms in VNS

B − VSFB . In other words, if firm A’s cost appears widely

uncertain to firm B, firm B would defer its investment. However, compared tothe case of constant demand, firm B now has stronger inventive to invest early,


as represented by the extra positive term, 7144rb σ 2

�. Hence, it becomes more likelythat the equilibrium would be (I, I) rather than (I, D). As proved analytically inAppendix C, we have the following result:

Proposition 2 (The effect of demand uncertainty): The introduction of stochasticdemand reinforces the benefits for firms A and B to invest early. Consequently,demand uncertainty, σ 2

�, makes equilibrium (I, I) more likely and (I, D) less likely.

This result may sound counterintuitive and different from the established decisiontheory about uncertainty. In the presence of uncertainty, a decision maker wouldnormally defer her decision in order to learn more information to resolve theuncertainty. But, our model shows that, if σ 2

� is sufficiently large, firms will find itoptimal to invest early.

The rationale can be explained as follows. Demand uncertainty, unlike costuncertainty, is a common uncertainty to both firms (while cost uncertainty is a pri-vate one). This common uncertainty gives firm B a fair chance to compete with firmA in a playfield that is made more even by the demand uncertainty. We mentionedearlier the real options view on uncertainty. Because firms can adjust their produc-tion quantity in the second period (after they have adopted the technology), theyessentially hold an option of scaling up or down the quantity depending on whetherthe demand goes up or down in the second period. The real options literatureshows that greater uncertainty actually increases the value of the option (Dixit &Pindyck, 1994; Zhu, 1999; Zhu & Weyant, 2003). Our result is consistent with thisview:

Corollary 2

Demand uncertainty tends to increase firms’ incentive to invest.

THE EFFECT OF ASYMMETRIC INFORMATION

We have looked at the adoption decisions under asymmetric information. It mightbe useful now to compare the equilibria under asymmetric information to thoseunder full information, so that we can better gauge the effects of informationasymmetry.

Adoption Patterns

Comparing the adoption patterns under asymmetric information and those un-der full information, we can see the effect of different information structures.Under symmetric information, the equilibrium of the adoption game exhibiteda simultaneous adoption pattern: both firms will either adopt the technology si-multaneously or the technology market remains inactive until the product marketdevelops more favorably. Under asymmetric information, we found that the adop-tion pattern can be very different from that under full information. The adoptionpattern becomes sequential (for a range of parameter values), as shown in Proposi-tion 1. This suggests that leadership may endogenously emerge from informationasymmetry.

Zhu and Weyant 657

For firm B, the thresholds of adopting the technology with full informationwould be:

�̄N S

B

∣∣ (cA = cL , FI) = 2cB − cL + 3√

rbI1 + r

�̄N SB

∣∣ (cA = cH , FI) = 2cB − cH + 3√

rbI1 + r

, (14)

With asymmetric information, the corresponding threshold from Proposi-tion 1 becomes:

�̄N SB

∣∣ (ξ, AI ) = 2cB − cL − ξ (cH − cL ) + 3√

rbI1 + r , (15)

where FI denotes “Full Information” and AI “Asymmetric Information.”�̄N S

B | (cA = cH , FI) stands for the adoption threshold conditional on firm B havingfull information and believing firm A’s cost is cH (ξ = 1). Similarly, �̄N S

B | (ξ, AI )represents the adoption threshold conditional on firm B’s belief that cA = cH withprobability ξ ∈ (0, 1). From this we have

∂�̄N SB

∣∣ (ξ, AI )

∂ξ= −(cH − cL ) < 0. (16)

Thus �̄N SB | (ξ, AI ) is a decreasing function of ξ , implying that firm B would invest

at a lower threshold (thus more aggressively) if it has a stronger belief that itscompetitor is a high-cost player. This aggressive behavior will make simultaneousadoption, (I, I), more likely.

Notice that (14) can be obtained from (15) by setting ξ = 0 and ξ = 1,respectively, making �̄N S

B | (cA = cH , FI) and �̄N SB | (cA = cL , FI) two extreme

values of �̄N SB | (ξ, AI ). Thus, the full-information thresholds are special cases of

the asymmetric-information threshold.It can be verified that

�̄N SB

∣∣ (cA = cH , FI) < �̄N SB

∣∣ (ξ, AI ) < �̄N SB

∣∣ (cA = cL , FI).

That is, the adoption threshold under asymmetric information, �̄N SB | (ξ, AI ), is

greater than �̄N SB | (cA = cH , FI) but lower than �̄N S

B | (cA = cL , FI). This occursbecause firm A not only tailors its adoption strategy to its own cost but also respondsto the fact that firm B has incomplete information and thus cannot do the same.If firm A’s cost is low, for example, it invests earlier; on the other hand, it waitslonger because it knows that firm B will invest at a lower threshold than firm Bwould have if it had full information about firm A’s low cost.

To sum up, information asymmetry is often combined with cost asymmetry inmany realistic settings. Allowing these two types of asymmetry to coexist makes themodel more realistic. Our analysis showed interesting dynamics by modeling thiscombination, where pure information asymmetry and pure cost asymmetry canbe considered special cases of the model. Clearly, informational advantage willalways amplify cost advantage. More interestingly, informational advantage tendsto mitigate the cost disadvantage in a subtle way that depends on the relative degreeof information asymmetry. In addition, the coupling of information asymmetry andcost asymmetry leads to another interesting dynamic to which we now turn.


Having Better Information Could Hurt You

We have seen above that asymmetric information about a rival’s cost introducesdifferent strategic dynamics to the technology adoption game. There is one morequestion that our model might be useful in answering; namely, is more informationalways better?

Under symmetric information, as documented in the existing literature onvalue of information, having more information can never make a firm worse off,since better information is always favorable in dealing with uncertainties (Horowitz,1970; Dasgupta & Stiglitz, 1980). However, it becomes subtler when firms haveasymmetric information in strategic games, especially when rivals have asymmetricinformation about a private parameter such as the postadoption cost that is directlylinked to their incentives to adopt the technology. We examine this question in thefollowing context: Firm A knows its true cost is low, that is, cA = cL, while firm Bonly has a probability distribution, that is, PB(cA = cH) = ξ and PB(cA = cL) =1 − ξ . Hence, the lower the ξ , the more accurate is firm B’s information about firmA’s cost. Both firms take this into consideration in making adoption decisions. Ouranalysis reveals a surprising result:

Proposition 3 (Having better information could hurt you): Having better infor-mation can lead to lower equilibrium profit under the following conditions: (1)The firm is uncertain about its competitor’s true cost; (2) The competitor knowsits true cost is low; (3) Both firms know this information structure and adjust theirbehavior accordingly.

As shown in Appendix D, a lower ξ (corresponding to better information) maycause two types of effects on firm B’s profits. (i) It may cause a shift of equilibriumin a direction that hurts firm B. From Proposition 1, ∂�̄H/∂ξ < 0; threshold �̄H

is a decreasing function of ξ . A lower ξ increases the upper threshold �̄H , hencecausing a shift of equilibrium from (I, I) to (I, D), thus reducing firm B’s profitableregion, as illustrated in Figure 4. (ii) A lower ξ may lead to lower incrementalprofits even when it does not cause the equilibrium to shift, that is, ∂V N S

B /∂ξ > 0.Both these effects are negative on firm B’s profit.

Figure 4: Better information may cause an equilibrium shift.

ξ (D (I, (I, I)

ΘΘ*

benefit firm A, hurt firm B

ξξ (D, D) (I, D) (I, I)

ΘΘ*

Firm B’s better information, represented by a lower ξ , may cause a shift of equilibrium in adirection that hurts firm B. Because the threshold �∗ is a decreasing function of ξ , a lowerξ increases the threshold �∗, hence causing the equilibrium region (I, I) to shrink, whichin turn reduces firm B’s profit.

Zhu and Weyant 659

The following intuition may help explain the rationale. If ξ is low, meaningthat firm B has fairly accurate information about firm A’s cost, this leads firm B tobehave conservatively in adopting the technology because it believes its competitoris strong (i.e., has low cost). On the other hand, if ξ is high, firm B confidentlybelieves that firm A is a weak rival (with high cost). This more “optimistic,” albeitless accurate, belief about its competitor’s cost leads firm B to behave aggressivelyin adopting the technology, which results in higher profit for firm B.

In terms of the example we mentioned in the Introduction, we could considerFord as firm A and GM as firm B. Prior experience with EDI gives Ford superiorinformation on the cost of the newer Internet-based B2B e-procurement systems.Its existing EDI network also allows Ford to enjoy a lower marginal cost afterimplementing the e-procurement system. In this case, if GM believes Ford’s newproduction cost is indeed low, it will behave more conservatively by producingand selling fewer cars to the automobile market (based on the rational assumptionsin a Cournot game). Ford knows this and thus behaves more aggressively. Thiswill lead to a lower profit, ceteris paribus, for GM than if it believes Ford’s costmight be not so low (i.e., poorer information about Ford’s cost reduction). Hence,a more accurate assessment of a competitor’s cost function actually leads to lowerequilibrium profit for GM.

Lower cost means a stronger competitor. When your competitor is strong, youwould rather not know this. The fundamental point is that information asymmetryhas changed the behavior of both competitors under these circumstances. Thus,having better information, or more precisely, having it known to the rival that onehas better information, may actually hurt a firm! The observation that firm B doesworse when it has better information illustrates an important difference betweensingle- and multi-agent decision problems.

Corollary 3

In conventional decision theory, having more information can never make thedecision maker worse off. However, in a multi-agent game-theoretic setting, havingmore information could make a player worse off.

CONCLUSIONS

Through introducing information asymmetry into technology adoption decisions,we have explored how asymmetric information brings additional dynamics in tech-nology adoption decisions beyond the full-information models typically consid-ered in the literature. We have found that adoption strategies under asymmetricinformation can be very different from those under full information. For example,equilibrium adoption patterns become sequential, which indicates that leadershipmay endogenously emerge from information asymmetry, even when it is balancedby conflicting forces such as a cost disadvantage. In contrast to conventional wis-dom, our model shows that common market uncertainty may actually induce firmsto act more aggressively under certain conditions. Our model also demonstrateshow information asymmetry on private costs would change the strategic behav-ior of both competitors, which leads to a surprising, but interesting result; namely,having better information could actually hurt a firm. A departure from conventional


decision theory, these results illustrate that different decision dynamics may arisein a game-theoretic setting with asymmetric information. In light of the signifi-cant amount of uncertainty that companies typically encounter about the outcomeof technology implementation in real business environments, the asymmetric in-formation setting appears to be more realistic than the typical full-informationassumption.

In today’s technology-based companies, innovations develop rapidly andmanagers constantly face adoption decisions. The ultimate goal of studying thetechnology-adoption game is to provide an underlying theory from which one maybetter understand strategic adoption decisions. A single model cannot answer allthe important questions, but we hope that the present model has generated somenew insights into the tradeoffs that shape technology leadership under asymmetricinformation. This seems to be particularly relevant to many situations involvinginformation technology where adoption decisions are frequently driven by com-petitive considerations. We hope this will motivate other researchers to engage infurther studies on these issues.

Indeed, we see this paper as an early attempt to understand the link betweentechnology adoption and asymmetric information. It leaves many issues open forfurther study. For example, the current model can be extended to study potentialsignaling strategies and gaming behavior—how firms with superior informationmay attempt to mislead competitors and alter the information structure. Also, tech-nology investments may produce multiple benefits beyond the cost dimension thatis considered in the current model, such as higher quality, faster delivery, and bettercustomer services. A more general reward function may be required to incorporatethese factors. The current study provides a base on which more sophisticated mod-els can be built. We keenly anticipate others’ ideas and efforts to pursue relatedresearch. [Received: August 2002. Accepted: August 2003.]

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APPENDIX A

Derivation of Equilibrium Quantities and ProfitsSimultaneous Decisions

When firms choose quantities simultaneously, they engage in a Cournot game. Wesolve for the optimal quantities in the Cournot-Nash equilibrium by following thestandard game theory approach (Fudenberg & Tirole, 1991; Varian, 1992; Tirole,1988; Rasmusen, 1989). If firm A’s cost is cH , it will choose q∗

A(cH) to maximizeits profit:

MaxqA

πA(qA, qB | cH ) = MaxqA

[P(�, qA, qB) − cH ]qA. (A1)

Similarly, it will choose q∗A(cL) if its cost is cL:

MaxqA

πA(qA, qB | cL ) = MaxqA

[P(�, qA, qB) − cL ]qA. (A2)

where π i is firm i’s profit, and P(�, qA, qB) = � − b(qA + qB) as defined in thesection on model setup. Firm B, however, does not know firm A’s true cost. It hasto optimize its expected profit under this incomplete information. Firm B believesthat firm A’s cost is high with probability ξ and low with probability (1 − ξ ), asdefined in the section on model setup. Absent any further information, it thus shouldanticipate that firm A’s quantity choice would be q∗

A(cH) with probability ξ , andq∗

A(cL) with probability (1 − ξ ), respectively. Mathematically, firm B’s decision isto choose q∗

B so as to maximize its expected profit, that is,

MaxqB

πB(qA, qB | ξ )

= MaxqB

{ξ [P(�, qA(cH ), qB) − cB]qB + (1 − ξ )[P(�, qA(cL ), qB) − cB]qB}.(A3)

By following the standard Cournot approach (Varian, 1992, pp. 285–291;Rasmusen, 1989, pp. 309–313), the simultaneous solution of the first-orderconditions of (A1)∼(A3) yields the equilibrium quantities:{

q∗A = 1

3b

[� − 1

2 (3cA − 2cB + EB(cA))]

q∗B = 1

3b [� − 2cB + EB(cA)](A4)

Zhu and Weyant 663

and the corresponding profits:

{π∗

A = 19b

[� − 1

2 (3cA − 2cB + EB(cA))]2 = b

[q∗

A

]2

π∗B = 1

9b [� − 2cB + EB(cA)]2 = b[q∗

B

]2 (A5)

where cA = {cL , cH }, EB(cA) = ξcH + (1 − ξ )cL is the expected cost of firm A(from firm B’s perspective); q∗

i (and π∗i ) denotes optimal quantity (profit) for firm i

at equilibrium. Checking the second-order conditions confirms that these quantitiesindeed maximize the expected profits.

The profits in (A5) represent the cash flows generated by the new technologyin each production period. Suppose that the discount rate is r, the present valueof investing in the technology can be calculated by summing up the profit of theinitial period and the discounted cash flows of all future periods:

{V N S

A = 1 + r9br

[� − 1

2 (3cA − 2cB + EB(cA))]2 − I

V N SB = 1 + r

9rb [� − 2cB + EB(cA)]2 − I(A6)

where VNSi represents the present value of firm i under Nash-Cournot equilibrium

(NS).Recall that the game has two stages. Even though the investment stage ends

when both firms have invested, the technology, once installed, continues to generatecash flows for n periods in the production stage. Hence the present value of thefuture cash flows is V = ∑n

i=1πi

(1 + r )i − I . If n → ∞, then V = πir − I . Hence, we

have the results in (A6). This assumption, albeit simplistic, avoids the complicationof discounting (which is not a focus of this paper).

Sequential Decisions

If one firm acts before the other, the Stackelberg model would apply to this sequen-tial game. There are two possible sequences as specified below.

Sequence 1: The less-informed firm (B) moves first and the more-informedfirm (A) follows

Since firm B moves first, it is a tentative monopoly in the first period. Then firm Ainvests in the technology and joins the market as a Stackelberg follower. Using thebackward induction approach in game theory (Fudenberg & Tirole, 1991, pp. 72,92; Varian, 1992, p. 270), we first solve the follower’s decision and then the leader’sdecision in the following manner. Assuming the leader (firm B) has already decidedqB, the follower (firm A) will choose q∗

A to maximize its profit conditional on itscost function:

MaxqA(cH )

πA(qA, qB | cH ) = MaxqA(cH )

[P(�, qA(cH ), qB(qA)) − cH ]qA(cH )

MaxqA(cL )

πA(qA, qB | cL ) = MaxqA(cL )

[P(�, qA(cL ), qB(qA), ) − cL ]qA(cL )(A7)


Anticipating firm A’s above move, the leader’s decision is to choose q∗B to

maximize its expected payoff, that is,

MaxqB

πB(qA, qB | ξ )

= MaxqB

{ξ[P

(�, q∗

A(cH ), qB) − cB

]qB + (1 − ξ )

[P

(�, q∗

A(cL ), qB) − cB

]qB

}.

(A8)

Jointly solving (A7)∼(A8) yields the equilibrium quantities:{q SF∗

A = 14b [� − 2cA + 2cB − EB(cA)]

q SL∗B = 1

2b [� − 2cB + EB(cA)](A9)

and the corresponding equilibrium profits:{π∗

A = 116b [� − 2cA + 2cB − EB(cA)]2 = b

[q SF∗

A

]2

π∗B = 1

8b [� − 2cB + EB(cA)]2 = b[q SL∗

B

]2 (A10)

Similar to the first appendix section, the present value of investing in thetechnology can be computed by summing up discounted future cash flows:

V SFA = 1

16rb[� − 2cA + 2cB − EB(cA)]2︸︷︷︸

Stackelberg follower profit

−I (A11)

V SLB = 1

4b(� − cB)2︸︷︷︸

Monopoly profit

+ 1

8rb[� − 2cB + EB(cA)]2︸︷︷︸Stackelberg leader profit

−I (A12)

where VSLi and VSF

i represent the value for the Stackelberg leader (SL) and Stackel-berg follower (SF), respectively; the term, 1

4b (� − cB)2, represents the monopolyprofit that the SL earned in the first period. It might be helpful to recall from (3)in the body of the article, the investment outlay, I, grows at the same rate as thediscount rate so as to avoid incentives from possible change of investment cost.When discounted back to the present value, future investment cost remains thesame in terms of present value.

Sequence 2: The more-informed firm (A) moves first and the less-informedfirm (B) follows

Upon observing firm A’s quantity and inferring its private cost information, firmB chooses its own quantity to maximize its expected profit. Firm A’s move couldreveal to firm B two possibilities: firm A’s cost is high (cA = cH) or low (cA = cL).Conditional on cA = cH , firm B’s decision is:

MaxqB

πB(q∗

A(cH ), qB

∣∣ cA = cH) = Max

qB

[P

(�, q∗

A(cH ), qB) − cB

]qB . (A13)

Similarly, conditional on cA = cL, firm B’s decision would be:

MaxqB

πB(q∗

A(cL ), qB

∣∣ cA = cL) = Max

qB

[P

(�, q∗

A(cL ), qB) − cB

]qB . (A14)

Zhu and Weyant 665

Anticipating firm B’s above responses, firm A chooses q∗A(cH) when its true cost

is cH , that is,

MaxqA(cH )

πA(qA(cH ), q∗

B

∣∣ cA = cH) = Max

qA(cH )

[P

(�, qA(cH ), q∗

B(qA)) − cH

]qA(cH ),

(A15)

and q∗A(cL) when its true cost is cL, that is,

MaxqA(cL )

πA(qA(cL ), q∗

B | cA = cL) = Max

qA(cL )

[P

(�, qA(cL ), q∗

B(qA)) − cL

]qA(cL ).

(A16)

Solving these optimization problems jointly yields the following equilibriumquantities: {

q SL∗A = 1

2b (� − 2cA + cB)

q SF∗B = 1

4b (� − 3cB + 2cA)(A17)

The corresponding equilibrium profits are, respectively,{π∗

A = 18b (� − 2cA + cB)2

π∗B = 1

16b (� − 3cB + 2cA)2(A18)

Using the same discounted method above, the present value can be calculated as:

V SLA = 1

4b(� − cA)2︸︷︷︸

Monopoly profit

+ 18rb (� − 2cA + cB)2︸︷︷︸

Stackelberg leader profit

−I (A19)

V SFB = 1

16rb(� − 3cB + 2cA)2︸︷︷︸

Stackelberg follower profit

−I (A20)

Notice that cA is known this time, hence cA rather than E(cA) is contained inthe solution.

Finally, both firm A and firm B could defer the investment to the second pe-riod. This scenario is similar to the Nash-Cournot equilibrium in the first appendixsection (except they missed the first-period profit):{

V N S2A = 1

9rb

[� − 1

2 (3cA − 2cB + EB(cA))]2 − I

V N S2B = 1

9rb [� − 2cB + EB(cA)]2 − I(A21)

where V NS2i denotes the present value of firm i under Nash-Cournot equilibrium

when both firms invest in the second period (NS2). �


APPENDIX B

Derivation of Adoption Equilibria under Asymmetric Information(Proposition 1)

The Nash-Cournot equilibrium is achieved by interrelated best responses to eachother’s strategies, but for the sake of presentation, we show firm A’s strategy first,then firm B’s, as follows.

Firm A’s Strategy

Let’s consider firm A’s payoff under the following four scenarios, assuming firm B’sstrategy is given. Making use of the subgame equilibrium results in Appendix A, wecan compute firm A’s payoffs as follows under four different strategy combinationscorresponding to the four branches in Figure 2:

(i) VA(A invests | B invests) = V N SA = 1 + r

9rb [� − 12 (3cA − 2cB + EB(cA))]2

− I = (1 + r )br (q N S∗

A )2 − I ;

(ii) VA(A defers | B invests) = V SFA = 1

16rb (� − 2cA + 2cB − EB(cA))2 −I = b

r (q SF∗A )2 − I ;

(iii) VA(A invests | B defers) = V SLA = 1

4b (� − cA)2 + 18rb (� − 2cA + cB)2

− I = 14b (� − cA)2 + b

2r (q SL∗A )2 − I ;

(iv) VA(A defers | B defers) = V N S2A = 1

9rb [� − 12 (3cA − 2cB + EB(cA))]2

− I = br (q N S∗

A )2 − I .

where the superscripts NS, SL, SF, and NS2 denote the sequence of the game asNash, Stackelberg leader, Stackelberg follower, and deferred Nash equilibrium.

First, comparing (i) and (ii) yields

V N SA − V SF

A > 0, (B1)

which means that VA(A invests | B invests) > VA(A defers | B invests). Given thesetwo options, it is a dominant strategy for firm A to invest in the first period ratherthan defer to the second period.

Next, to compare (iii) and (iv), we have:

V SLA − V N S2

A = 1

4b

(� − cA

)2

+ b

r

(1√2

q SL∗A + q N S∗

A

)(1√2

q SL∗A − q N S∗

A

)(B2)

Its sign depends on the sign of ( 1√2q SL∗

A − q N S∗A ), as the other terms are positive.

1√2

q SL∗A − q N S∗

A = 3 − 2√

2

6√

2b

[� − (

6 + 3√

2)cA + cB + (

4 + 3√

2)EB(cA)

](B3)

If cA = cL, it can be shown:

V SLA − V N S2

A > 0, if cA = cL . (B4)

which means that, if cA = cL, firm A would rather like to be a Stackelberg leaderthan split the market with firm B.

Zhu and Weyant 667

If cA = cH , it can be shown, based on (B2) and (B3),

V SLA − V N S2

A > 0, if � ≥ �̄b and cA = cH (B5)

where

�̄b = (6 + 3

√2)cH − cB − (

4 + 3√

2)EB(cA). (B6)

Firm A would invest when demand is high enough (i.e., � ≥ �̄b).However, if � < �̄b, VSL

A − V NS2A < 0. Firm A would defer its investment

under the conditions of high cost (i.e., cA = cH) and low demand (i.e., � < �̄b).This result can be compared to the result above in (B4) where a low-cost firm Awould always want to invest. Together these results lead to a separating equilibriumin the sense that firm A defers only when it is a high-cost firm.

The incentive for firm A to defer was believed to be to hide its cost by movingafter firm B. Unfortunately, since firm A defers only when it is a high-cost firm,firm B can infer that by observing the fact that firm A defers. Consequently, firmA cannot hide its cost by deferring, as this action itself would reveal informationto its competitor. By deferring, firm A would still reveal its cost, but it gets lowerprofit than being a Stackelberg leader. Knowing this tradeoff, firm A would investin the first period (as long as demand is above a certain threshold, which will bespecified later).

Firm B’s Strategy

Having analyzed firm A’s strategy, we now turn to firm B’s payoffs. Our analysisabove shows that firm A would rather invest than defer. Then firm B only needs tocompare its payoffs conditional on “firm A invests”:

(i) EB[VB(B invests | A invests)] = E(V N S

B

) = 1 + r

9rb[� − 2cB + EB(cA)]2 − I

= (1 + r )b

r

(q N S∗

B

)2 − I,

(ii) EB[VB(B defers | A invests)] = E(V SF

B

) = 1

16rb[� − 3cB + 2EB(cA)]2

+ 1

4rbσ 2

c − I = b

r

[EB

(q SF∗

B

)]2 + 1

4rbσ 2

c − I

where termσ 2c = var(cA) is introduced to account for the effect that cA is a stochastic

variable to firm B. To compare firm B’s payoffs in these two scenarios, we have:

E(V N S

B

) − E(V SF

B

) = 1

9b[� − 2cB + EB(cA)]2

+ 1

144rb[7� − 17cB + 10EB(cA)]

× [� − 2EB(cA) + cB] − 1

4rbσ 2

c (B7)


Solving this equation, E(VNSB ) − E(VSF

B ) = 0, yields two roots, but only one ofthem is meaningful:

�̄2 = 1

7 + 16r

[(5 + 32r )cB + 2(1 − 8r )EB(cA)

+ 6√

4(1 + r )(cB − EB(cA))2 + (7 + 16r )ξ (1 − ξ )(cH − cL )2]

(B8)

Because (B7) is a convex function, then

E(V N S

B

) − E(V SF

B

) ≥ 0, if � ≥ �̄2. (B9)

Equilibrium Analysis

Having examined firm A’s and firm B’s strategies, we can build on these results toexamine the equilibria of the investment game. Both firms compare the payoffs fromtheir strategy sets. The strategy that gives the optimal payoff, given the competitor’saction, will constitute a Nash equilibrium. Here it gets more complicated becausewhether (B7) is positive or negative depends on the combination of several factors.For ease of comparison, we divide the demand spectrum into several regions andanalyze the equilibrium within each region.

(A) If demand is sufficiently high, Θ≥ Θ̄H, the equilibrium is (I, I)

An (I, I) equilibrium will require that all of the following conditions be met:

V N SA > 0 ⇒ � > �̄N S

A = 1

2[3cA − 2cB + EB(cA)] + 3

√rbI

1 + r

V N SB > 0 ⇒ � > �̄N S

B = 2cB − EB(cA) + 3

√rbI

1 + r

V N SA − V SF

A > 0 (satisfied as proved in (B1))

V N SB − V SF

B > 0 ⇒ � > �̄2 (from (B9))

where �̄N Si denotes the threshold of demand that will make firm i’s value positive

under Nash-Cournot equilibrium (NS). Similar notations are used below wherethe superscript stands for the sequence of the game, that is, NS, SL, SF, NS2, andMONO (for monopoly). For notational convenience, define

�̄H = max{�̄N S

A , �̄N SB , �̄2

}= max

{1

2[3cA − 2cB + EB(cA)] + 3

√rbI

1 + r, 2cB − EB(cA) + 3

√rbI

1 + r, �̄2

}(B10)

If � ≥ �̄H , firm A and firm B will prefer to invest, leading to an (I, I) equilibrium.

Zhu and Weyant 669

(B) If demand is moderate, Θ̄L ≤Θ< Θ̄H, the equilibrium is (I, D)

If demand is lower than �̄H , an (I, D) equilibrium may result if the followingconditions are met:

V SLA > 0 ⇒ � > �̄SL

A

= 1

1 + 2r

(2(1 + r )cA − cB +

√8br I (1 + 2r ) − 2r (cB − cA)2

)V SF

B > 0 ⇒ � > �̄SFB = 3cB − 2cA + 4

√rbI

V SLA − V N S2

A > 0 (satisfied if cA = cL , or if cA = cH and � ≥ �̄b)

V SFB − V N S

B ≥ 0 ⇒ � ≤ �̄2 from (B9)

Define

�̄L = max{�̄SL

A , �̄SFB , �̄b

}. (B11)

In this region, firm B cannot be profitable if both firms invest. Thus B will notinvest if B believes that A is going to invest. Since firm B cannot make a profit inthis region unless firm A stays out, but firm A is not going to stay out, firm B willnot invest. Because firm A’s threshold is lower than firm B’s, firm A’s incentive toinvest early is stronger than firm B’s. Thus it is impossible for firm A to wait andallow firm B to invest first and become a leader.

(C) If demand is low, Θ̄L2 ≤Θ< Θ̄L, the equilibrium may be (D, D)

Based on the above analysis, firm A would rather invest in the first period thandefer, if cA = cL or if cA = cH and � ≥ �̄b. This makes the (D, D) equilibriuminfeasible if cA = cL. Only when cA = cH , a (D, D) equilibrium is possible, whichwould require the following conditions:

V N S2A > 0 ⇒ � > �̄N S2

A = 12 (3cA − 2cB + EB(cA)) + 3

√rbI

V N S2B > 0 ⇒ � > �̄N S2

B = 2cB − EB(cA) + 3√

rbI

V SLA − V N S2

A < 0 ⇒ � < �̄b

Define

�̄L2 = max{�̄N S2

A , �̄N S2B

}(B12)

(D) If demand is very low, Θ̄min ≤Θ< Θ̄L2, the equilibrium may be (I, N)or (N, I)

If demand is further lower, then V NS2A < 0 or V NS2

B < 0, but V MONOA > 0 and VMONO

B >

0, which means that the market may accommodate only one firm. If both invest,they will end up losing, but if only one firm invests and stays in the market, eitherone of them is profitable. There are two Nash equilibria in this scenario: (I, N) and(N, I), where N denotes “Not invest.” If V MONO

A (cA = cL) > 0 and VMONOB ≤ 0, then


firm A invests and enjoys being a monopoly in the market because of its low cost.This results in an (I, N) equilibrium. On the other hand, if V MONO

A (cA = cH) < 0but VMONO

B > 0, then firm B invests as a monopoly, leading to a (N, I) equilibrium.Define

�̄min = min{�̄MONO

A , �̄MONOB

} = min

{cA + 2

√brI

1 + r, cB + 2

√brI

1 + r

}(B13)

If � < �̄MONOmin , the market demand is so low that even a monopoly cannot be

profitable. This results in a (N, N) equilibrium. Market becomes inactive. �

APPENDIX C

The Effect of Demand Uncertainty (Proposition 2)

The demand is modeled as a simple stochastic binomial variable. That is, thedemand starts with � in the first period and could move up to u� with probabilityp or down to d� with probability 1 − p in the second period, where u and d are themultiplicative parameters of a binomial process (u > 1 and d < 1), as illustratedin Figure 3. It can be shown that u and d are related to σ of �. The relationship isdetermined by: u = eσ

√t and d = e−σ

√t (see Luenberger, 1998, pp. 313–315 for

a proof). To keep the model simple, we assume that the demand stays at either u�

or d� beyond the second period so that future cash flows generated by the newtechnology can be reasonably computed.

Following a similar structure to Appendix B, we analyze firm A’s strategyfirst, then firm B’s, even though the Nash-Cournot equilibrium is really achievedby interrelated best responses to each other’s strategies.

Firm A’s Strategy

Similar to Appendix B, we first consider firm A’s payoff under the following fourscenarios:

(i) E(V N S

A

) = 1

9b

[� − 1

2(3cA − 2cB + EB(cA))

]2

+ 1

9rb

[E�̃ − 1

2(3cA − 2cB + EB(cA))

]2

+ 1

9rbσ 2

� − I

(C1)

(ii) E(V SF

A

) = 1

16rb(E�̃ − [2cA − 2cB + EB(cA)])2 + 1

16rbσ 2

� − I (C2)

(iii) E(V SL

A

) = 1

4b(� − cA)2 + 1

8rb(E�̃ − 2cA + cB)2 + 1

8rbσ 2

� − I (C3)

(iv) E(V N S2

A

) = 1

9rb

[E�̃ − 1

2(3cA − 2cB + EB(cA))

]2

+ 1

9rbσ 2

� − I (C4)

where �̃ represents the stochastic demand with expected value, E�̃, andvariance,var(�̃) = σ 2

�. Both can be computed from known parameters, �, u, d,and p. Notice that the extra term σ 2

� in each equation above is due to the stochastic

Zhu and Weyant 671

nature of the demand. If we set σ 2� = 0, the above four equations become the same

as those in Appendix B.Because 1 + r

9rb σ 2� > 1

16rb σ 2� and 1

8rb σ 2� > 1

9rb σ 2�, it can be shown the results in

Appendix B still holds:{E

(V N S

A

)> E

(V SF

A

)E

(V SL

A

)> E

(V N S2

A

), if cA = cL

(C5)

Thus the introduction of stochastic demand does not qualitatively alter the firms’strategies. In fact, because of the relative strength of the extra σ 2

� terms, i.e.,1 + r9rb σ 2

� > 116rb σ 2

� and 18rb σ 2

� > 19rb σ 2

�, it reinforces the benefits for firm A to investearly. Thus, compared to the situation in Appendix B, firm A has an even strongerincentive to invest in the first period.

Firm B’s Strategy

Having analyzed firm A’s strategies, we now consider firm B’s payoffs. Given theabove result, firm B only needs to compare the values of the following two options:

(i) E(V N S

B

) = 1

9b[� − 2cB + EB(cA)]2 + 1

9rb[E�̃ − 2cB + EB(cA)]2

+ 1

9rbσ 2

� − I

(ii) E(V SF

B

) = 1

16rb[E�̃ − 3cB + 2EB(cA)]2 + 1

16rbσ 2

� + 1

4rbσ 2

c − I

where two variance terms, var(cA) = σ 2c and var(�̃) = σ 2

� account for the effects ofthe two stochastic variables, because firm B now faces two types of uncertainties—demand uncertainty and cost uncertainty. To compare (i) and (ii), we have

E(V N S

B

) − E(V SF

B

) = 1

9b[� − 2cB + EB(cA)]2

+ 1

144rb[7E�̃ − 17cB + 10EB(cA)]

× [E�̃ + cB − 2EB(cA)] + 7

144rbσ 2

� − 1

4rbσ 2

c(C6)

All other terms are positive, hence its sign depends on the sign of

= 7

144rbσ 2

� − 14rb σ 2

c , (C7)

namely, the relative degree of demand uncertainty and cost uncertainty. The formerworks to the advantage to firm B (as it deters its rival from being aggressive), butthe latter works as the informational disadvantage to firm B.

Severe information asymmetry, as represented by − 14rb σ 2

c , may offset thepositive terms in (C6). In other words, if firm A’s cost appears widely uncertainto firm B, firm B would defer its investment. However, compared to the case of


constant demand as analyzed in Appendix B, firm B now has stronger inventive toinvest early, as represented by the extra positive term, 7

144rb σ 2�. Hence, it becomes

more likely that the equilibrium would be (I, I) rather than (I, D).This is indeed confirmed by our analysis. If both firm A and firm B are

profitable (i.e., � is above a certain level), and if the information asymmetry is notsevere, then firm B would prefer to invest. To see why, let E�̃ = � and compare(B7) and (C6), we find that the difference between (B7) and (C6) is the positiveterm 7

144rb σ 2�, which may make (C6) to be positive even when (B7) is negative.

Thus, the demand uncertainty does not qualitatively change the dominant strategyof firm A but makes firm B more aggressive. �

APPENDIX D

Derivation of Proposition 3

A lower ξ (corresponding to better information) may induce two types of effectson firm B’s profits, as illustrated in Figure 4. (i) It may cause a shift of equilibriumin a direction that hurts firm B; and (ii) it may lead to lower incremental profitseven when it does not cause the equilibrium to shift. Below we show these twoeffects respectively. First we consider how the change of ξ may affect firm B’sinvestment decision (i.e., equilibrium shift). Next, we consider the situation thatif firm B has already decided to make investment in the first period, how betterinformation affects its payoff (i.e., incremental change).

(i) Equilibrium shift: From Proposition 1, the threshold for simultaneousinvestment is �̄H , which is defined in (B10). If � ≥ �̄H , firm A and firm B willprefer to invest, leading to an (I, I) equilibrium. If cA = cL, �̄H = max{�̄N S

B , �̄2},where �̄N S

B and �̄2 are determined in Appendix B. By taking first derivative withrespect to ξ , it can be shown:

∂�̄N SB

∂ξ= −(cH − cL ) < 0 (D1)

∂�̄2

∂ξ= 1

7 + 16r(cH − cL )

×[

2(1 − 8r ) − 3[8(1 + r )cB + 3(2 + 8r )EB(cA) − (7 + 16r )(cH + cL )]√4(1 + r )(cB − EB(cA))2 + (7 + 16r )ξ (1 − ξ )(cH − cL )2

]< 0

(D2)

Obviously, threshold �̄H is a decreasing function of ξ . Based on Proposition 1,firm B can expect positive profit under equilibrium (I, I) in the demand region� ≥ �̄H . Hence, shrinking this region would reduce firm B’s profitable region.Based on (D1), a lower ξ leads to a higher �̄H ; a higher �̄H in turn leads to asmaller (I, I) region, which eventually reduces firm B’s profit. As illustrated inFigure 4, a lower ξ increases the upper threshold �̄H (but it has no effect on thelower threshold, �̄L ), hence, causing a shift of equilibrium from (I, I) to (I, D).This hurts firm B’s profit.

Zhu and Weyant 673

(ii) Incremental change: Among the four equilibrium regions discussed inAppendix B, region (I, I) is the best region in which firm B’s profit will be thehighest. Moreover, as shown in Appendix B,

V N SB = 1 + r

9rb[� − 2cB + EB(cA)]2 − I = (1 + r )b

r

(q N S∗

B

)2 − I.

Taking first derivative with respect to ξ , we get

∂V N SB

∂ξ= 2(1 + r )[� − 2cB + ξcH + (1 − ξ )cL ]

9rb(cH − cL )

= 2(1 + r )

3r

(q N S∗

B

)(cH − cL ) > 0 (D3)

Thus, a lower ξ (better information) leads to a lower profit for firm B. Therefore,better information can hurt firm B even within the same equilibrium region. �

LIST OF NOTATIONS

ci Marginal cost for firm i, after adopting the technology.

cH High marginal cost.

cL Low marginal cost.

ξ Probability that firm B believes firm A’s cost is high, thatis, PB(cA = cH) = ξ , where ξ ∈ [0, 1].

EB(cA) Firm B’s belief about firm A’s cost, EB(cA) = ξcH +(1 − ξ )cL.

σ 2c Variance of cost, var(c) = σ 2

c .

P Price of the product.

b Demand elasticity parameter.

r Discount rate.

I Investment outlay to adopt the new technology.

qi Quantity of the product produced by firm i, (i = A, B).

q∗i Optimal quantity at equilibrium.

� Demand intercept.

�̃ Stochastic demand.

σ 2� Variance of stochastic demand, var(�̃) = σ 2

�.

u, d Multiplicative parameters of the demand binomial process(u > 1 and d < 1).

π i Profit stream for firm i in each period.

π∗i Profit stream at equilibrium.

VNSi Present value of future profit streams, where the subscript

denotes the firms and the superscript represents the equi-librium paths, where NS, SL, SF, NS2, MONO denoteNash, Stackelberg leader, Stackelberg follower, deferredNash equilibrium, and monopoly, respectively.


�̄N Si Threshold of demand that makes firm i’s value positive

under Nash-Cournot equilibrium (NS). Similar notationsare used for other equilibria where the superscripts SL,SF, NS2, MONO denote Stackelberg leader, Stackelbergfollower, deferred Nash equilibrium, and monopoly, re-spectively.

(I, D) Strategy pair, meaning firm A invests (I) while firm Bdefers (D). Similar notation for (I, I), (D, I), (D, D),(I, N) and (N, I), where I = Invest, D = Defer, and N =Not invest.

FI Full Information.

AI Asymmetric Information.

�̄N SB | (cA = cH , FI) Threshold conditional on firm B having full information

and believing firm A’s cost is cH .

�̄N SB | (cA = cL , FI) Threshold conditional on firm B having full information

and believing firm A’s cost is cL.

�̄N SB | (ξ, AI ) Threshold conditional on firm B’s belief that cA = cH with

probability ξ ∈ (0, 1).

Kevin Zhu received his PhD from Stanford University and is currently an as-sistant professor of information systems in the Graduate School of Management,University of California, Irvine. His dissertation was titled “Strategic Investmentin Information Technologies: A Real-Options and Game-Theoretic Approach,” inwhich he pioneered an innovative approach that integrated real options and gametheory for modeling investment strategies under competition. His current researchfocuses on strategic investment in information technologies, economics of infor-mation systems and electronic markets, economic and organizational impacts of in-formation technology, and information transparency in supply chains. His researchmethodology involves game theory, economic modeling, and empirical analysis.His work has been accepted for publication in journals such as Management Sci-ence, Information Systems Research, European Journal of Information Systems,Decision Sciences, Electronic Markets, and Communications of the ACM. One ofhis papers has won the Best Paper Award of the International Conference on Infor-mation Systems (ICIS), 2002. He was the recipient of the Academic AchievementAward of Stanford University, the Faculty Research Award of the University ofCalifornia, and the Charles and Twyla Martin Excellence in Teaching Award. Seemore information at http://web.gsm.uci.edu/kzhu/.

John P. Weyant is professor of management science and engineering at StanfordUniversity, a senior fellow in the Institute for International Studies, and directorof the Energy Modeling Forum (EMF) at Stanford University. Professor Weyantearned a BS/MS in aeronautical engineering and astronautics, MS degrees in engi-neering management and in operations research and statistics all from RensselaerPolytechnic Institute, and a PhD in management science with minors in economics,operations research, and organization theory from the University of California at

Zhu and Weyant 675

Berkeley. His expertise areas include strategic decision making, financial model-ing, options, policy, and strategy. His current research focuses on economic mod-els for strategic planning, competition, and investment in high-tech industries, andanalysis of global climate change policy options. He is on the editorial boards ofIntegrated Assessment, Environmental Management and Policy, and The EnergyJournal and a member of INFORMS, the American Economics Association, andAmerican Finance Association.

strategic decisions of new technology adoption under...

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