Strategic Decisions of New Technology Adoption Under Asymmetric Information: a Game-Theoretic Model∗

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

Strategic Decisions of New Technology Adoption 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. Weyant Room 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 using economic analysis. We show how asymmetric information affects firms’ decisions to adopt 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 information structures under which two competing firms have asymmetric information about the future performance (i.e., postadoption costs) of the new technology. We find that equilibrium strategies under asymmetric information are quite different from those under symmetric information. Information asymmetry leads to different incentives and strategic behaviors in the technology adoption game. In contrast to conventional wis- dom, our model shows that market uncertainty may actually induce firms to act more aggressively under certain conditions. We also show that having better information is not always a good thing. These results illustrate a key departure from established decision theory. 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: Economic Analysis and Game Theory.

∗We are grateful to Robert Wilson, William Sharpe, Haim Mendelson, Hau Lee, James Sweeney, and Blake Johnson for valuable suggestions on our initial work of this research at Stanford University. We subsequently received constructive comments from Vijay Gurbaxani, Rajeev Tyagi, Sajeev Dewan, Barrie Nault, 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 computer technologies, has heightened the strategic importance of new technologies in a competitive marketplace (Porter & Millar, 1985). In today’s technology-driven economy, new innovations develop rapidly, and managers constantly face adoption decisions. Companies often invest in new technologies in the hope to gain an edge over their competitors (Clemons, 1991; Parsons, 1984). A survey shows that 50% of technology executives indicated that to “gain competitive advantage” was the top priority that influenced their organization’s increase in Internet-based technology investment, and 21% believed that “responding to a competitor” was also a key factor (Goldman Sachs, 2000). In an oligopolistic industry, one firm’s technology adoption decision could affect the market structure and strategic equilibrium. While the tangible value (e.g., improvement in productivity and operational efficiency) of new technologies has been the focus of the literature, a few recent studies show that a major driver of investment in technology lies in the strategic value gained from altering the competitive 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 critical to the firm’s ability to compete in the product market. Our model will abstract away from specific technologies, though information technologies seem to exhibit these features more often than traditional technologies. Their deployment often helps 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 and Gateway are leveraging their investments in Internet-based supply chain systems to gain advantages over competitors. In addition to these examples, successful strategic applications of new technology in achieving competitive gains are abun- dantly documented in the literature, including American Airline’s SABRE computer reservation system, Wal-Mart’s inventory information system, and FedEx’s package tracking system (Clemons, 1991). A common benefit of these adoptions is the 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 to compete in the market. These examples also illustrate that technology adoption decisions are often made under strategic considerations or competitive pressure. Indeed, in an oligopolistic industry with several competitors, adopting a new technology is a strategic decision. On the one hand, facing uncertainty about the new technology, each firm has an incentive to delay the adoption decision until it receives more information to resolve uncertainties about the new technology’s cost and performance. On the other hand, if it does so, it runs the risk that another firm may preempt it by adopting first because technological investments often exhibit early mover 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 by a rival creates incentives to act quickly. This dilemma is especially important when the market is volatile and the future performance of the new technology is uncertain. Thus, the tradeoff between adopting early and waiting for more information elevates the strategic importance of leader-follower dynamics. What makes these decision dynamics more complicated, yet more interesting, is information asymmetry across firms. Information asymmetry arises when one firm has more information than others. This may be due to factors such as prior investment in related technologies (the learning effect), information-gathering activities, or in-house knowledge about the implementation process. Real-world observation has provided us with many situations in which companies are indeed asymmetrically informed. For example, Dell Computer may have better information on the cost structure of the “build-to-order” model than traditional PC makers such as IBM and Compaq (now Hewlett-Packard [HP]). A firm such as Ford that has experienced similar technologies (e.g., EDI) may know more about the cost functions of Internet-based e-procurement technologies than a firm without such experience. The existence of information asymmetry may have significant effects on technology adoption decisions in an oligopolistic industry, although it is unclear what 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 attempt to invest in a new computerized technology that will enable them to produce a new product and serve a new market segment. However, their technology-adoption efforts may involve technical uncertainty in the sense that implementation of the new 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 about the implementation process, one firm (say, firm A) has superior information about the true cost function associated with the new technology. That is, firm A knows something that firm B does not know. Hence, information is asymmetric across these two firms. Motivated by these kinds of strategic considerations, we study the link between technology adoption decisions and the information structure under which the decisions are being made. Our research questions are: (1) What happens to the adoption decisions if firms have asymmetric information regarding the future performance of a new technology? (2) Under what conditions will firms adopt the technology early, and under what conditions will they wait and allow their competitor to become a leader? (3) What is the effect of market uncertainty on the adoption pattern? and (4) Is having more information always a good thing in technology adoption games? To better understand these issues, we build a simple model with stylized parameters, 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 focus on a two-stage adoption game between two competing firms. First they invest in capability in the first stage, and then optimally exploit the capability in the second stage, contingent on the technology having been implemented. Naturally, 646 Strategic Decisions of New Technology Adoption 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 this early 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 learn from the other firm’s adoption decisions. In this setting, the better-informed firm learns less from the other firm’s actions, and often chooses to move first, even when it suffers cost disadvantage. The less-informed firm may actually prefer to be a follower, willing to sacrifice the early-mover advantage, since the benefits of learning from the leader’s actions may outweigh the costs of “Stackelberg followership.” Thus, a leader-follower dynamic may be induced endogenously by the information asymmetry.

Relationship to the Literature Our study is related to several streams of literature in technology adoption, research and development (R&D) innovations, economics, and information technology. The game-theoretic literature on technological competition has demonstrated that the adoption of a new technology often exhibits a preemptive feature—each firm tries to preempt its rivals by investing early (Fudenberg & Tirole, 1985; Katz & Shapiro, 1986; Dasgupta & Stiglitz, 1980; Reinganum, 1985; and Spence, 1985). While stressing 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 a real options perspective, viewing investment projects as real options. The opportunity to adopt a new technology is equivalent to a call option with an exercise price equal to the investment outlay, and the underlying asset is the new technology. Several studies view technology investments as real options, including Kambil, Henderson, and Mohsenzadeh (1993), Benaroch and Kauffman (1999), Zhu (1999), and Tallon, Kauffman, Lucas, Whinston, and Zhu (2002). These studies documented the crucial role of flexibility in investment decisions under uncertainty. Yet the real options literature has been typically based on two specific assumptions: (a) the firm has a monopoly power over an investment opportunity, and (b) the product market is perfectly competitive. As a result, investment does not affect product market competition. In contrast to the technological competition literature that focuses on preemption, the real options literature stresses the option value to wait, but ignores the risk of competitive preemption. In the adoption literature related to information technologies, several studies focus on the possibility of gaining a competitive advantage via the impact on market structure of interorganizational systems (IOS). Among others, Barua and Lee (1997), Riggins et al. (1994), and Wang and Seidmann (1995) studied EDI adoption strategies and competitive effects. They analyzed the introduction of EDI in a vertical market involving a single manufacturer and several suppliers, where the manufacturer faces a linear demand curve and the competing suppliers have upward-sloping marginal cost functions. They demonstrated that a supplier might have to join the EDI network out of competitive pressure or “strategic necessity.” Zhu and Weyant 647

These papers substantially improved our understanding about strategic decision making in technology adoption. Yet, a common assumption made in the literature is symmetric information. That is, ﬁrms have symmetric information sets and no private information is involved. We build on these studies, particularly the game-theoretic modeling of IOS, and address additional concerns arising from information asymmetry, an issue on which the literature has not yet focused. As we shall see, information asymmetry leads to different incentives and strategic behaviors in the technology adoption game. By relaxing the typical full-information assumption in the literature, our model allows us to gauge the effect of information asymmetry on technology adoption decisions and to show how asymmetric information alters the adoption equilibrium. The remainder of this paper proceeds as follows. The next section describes the basic setup of the model. The third section derives the subgame equilibrium quantities and adoption decisions under asymmetric information. The fourth section explores the effects of information asymmetry on adoption decisions where, we show that, having better information is not necessarily better. A ﬁnal section concludes the paper. We emphasize the results in the text and relegate the technical proofs to the appendices. For readers’ convenience, a list of notations is summarized at the end of the paper.

THE MODEL SETUP In this section, we construct a two-stage game-theoretic model. We try to keep the model simple so that we can focus on the key issues identified above. In a duopoly industry that consists of two companies, competition proceeds in two constituent 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.

{I, D} Firm A Tech qA

cA Product Market qB {I, D} Θ=Θ−+ Firm B Tech cB Pqqiij(,, ) bqq ( ij )

Adoption 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 compete in the same product market. Revenues are realized according to the resulting Nash-Cournot equilibrium. 648 Strategic Decisions of New Technology Adoption new technology that will enable the firm to produce a product and serve a new market in the second stage. The strategic impact of technology adoption in the first stage is captured through its impact on competitive reactions and equilibrium payoffs. 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 technology that requires a lumpy investment outlay, I.Ifafirm decides to adopt the technology, it also needs to decide, at the second stage, how many units of the product to produce, that is, a quantity qi that maximizes its expected payoff. Payoffs: The payoff to firm i is a function of the strategies chosen by it and its competitor. If both firms make decisions simultaneously (without observing each other), they will split the market according to a Nash-Cournot equilibrium. If one firm adopts first and the other does later, their payoffs will be determined 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 investment stage lasts for two periods and the adoption game ends after the second period or when both firms have invested, whichever happens first. The technology, once installed, continues to generate cash flows for n periods in the production stage. 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 these two periods (N), which means the firm drops out of the market with no capability to compete in the market stage.

Figure 2: The game tree.

Outcome Payoffs

NS NS (I, I) VVAB, I A D VVSF, SL I (D, I) AB

B SL SF (I, D) VVAB, D I A

D NS22 NS (D, D) VVAB,

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), NS NS they receive payoffs VA and VB 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 represented 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 supplied by firms i and j respectively; b is a constant representing demand elasticity; is the demand intercept. We will consider two situations: constant demand first and stochastic demand ˜ in later sections. A firm’s cost function is determined by its technology. The cost function for firm 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). In addition 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 change of investment cost, we assume that the investment outlay grows at the same rate as the 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 may arise, we abstract from other possibilities and focus on asymmetric information about cost so that we can isolate the role of asymmetric information in technology adoption 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 the extent that other benefits can be translated into equivalent cost impacts (i.e., better quality or service can be translated into lower cost in the sense that a firm needs to equalize the same level of quality or service at some extra cost). Therefore, analogous results could be obtained if the investment results in greater product quality or better customer service. See Spence (1985) for an analytical formulation of this view. Specifically, the asymmetric information is defined as follows: (i) Firm A has full information on both firms’ cost functions (status quo in literature).

(ii) Firm B knows its own cost function, cB, but has incomplete information about ﬁrm A’s cost function. Firm B depicts this incomplete information by the following probability distribution: cH with probability ξ E B (cA) = (4) cL with probability (1 − ξ)

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 650 Strategic Decisions of New Technology Adoption

σ 2 ξ variance, c. As we can see, probability is essentially a measure of ﬁrm B’s belief, which represents a standard Bayesian assessment of the chance that the competitor’s cost is high.

(iii) The parameters ξ, cH, cL, and cB are common knowledge, while firm A’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 postadoption ξ σ 2 cost, thus information is asymmetric. The asymmetry is captured by and c . This simple model is a modest departure from the literature where both firms had symmetric information.

ANALYSIS OF ADOPTION DECISIONS To analyze the two-stage game, we first need to derive the subgame equilibrium quantities and payoffs for the second stage, assuming that the technology has been put 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 induction solution method well known in game theory (Fudenberg & Tirole, 1991). We now focus on the second-stage subgame equilibrium quantities and profits.

Optimal Quantities and Equilibrium Proﬁts There are two possible situations in the second-stage competition: simultaneous and sequential moves.

Simultaneous moves Firms A and B simultaneously decide the quantity of product to produce. Since firm A knows its own cost function, it will choose a quantity, conditional on its true cost, that maximizes its expected profit. Naturally, firm A may want to choose a lower quantity if its marginal cost is high than if it is low. Firm B, for its part, should anticipate that firm A will tailor its quantity to its costs in this way. However, firm B has only a probability distribution on firm A’s cost. It has to optimize its profit ∗ ∗ under 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: ∗ 1 1 q = − (3cA − 2cB + E B (cA)) A 3b 2 (5) ∗ = 1 − + qB 3b [ 2cB E B (cA)] The corresponding equilibrium profits are, respectively, π ∗ = 1 − 1 (3c − 2c + E (c )) 2 A 9b 2 A B B A (6) π ∗ = 1 − + 2 B 9b [ 2cB E B (cA)] 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 if its own cost is lower or rival’s cost is higher. Equation (5) can be written as   ∗ = 1 − + + 1 − ξ − qA(cH ) 3b ( 2cH cB ) 6b (cH cL ) ξ q∗ (c ) = 1 ( − 2c + c ) − (c − c )  A L 3b L B 6b H L ∗ = 1 − + ξ + − ξ qB 3b [ 2cB cH (1 )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 qi 1 − + 3b ( 2ci c j ) (Varian, 1992, p. 285–291). Under asymmetric information, ∗ 1 − + ∗ 1 − + q A(cH) is greater than 3b ( 2cH cB ) and q A(cL) is less than 3b ( 2cL cB ). This occurs because both firms not only tailor their production decisions to their own costs but also respond to the competitor’s adjustments resulting from the information asymmetry. This illustrates that strategic interactions affect production decisions, where not only a firm’s own cost parameter but also the competitor’s cost parameter enter their decisions as shown in (5). The profits in (6) represent the cash flows generated by the new technology in each production period. Recall that the discount rate is r, the present value of investing in the technology can be calculated by summing up the profit of the initial period and the discounted cash flows of all future periods, minus the investment outlay: V NS = 1 + r − 1 (3c − 2c + E (c )) 2 − I A 9br 2 A B B A (7) NS = 1 + r − + 2 − VB 9rb [ 2cB E B (cA)] I NS where Vi represents the present value of firm i under Nash-Cournot equilibrium (NS).

Sequential moves Under asymmetric information, the order of sequential moves may reveal private information. Firms can infer information by observing other firms’ actions. The sequencing of moves becomes subtler, as it reflects each firm’s calculated tradeoff between the early mover advantage and the informational benefit of waiting to learn rival’s private information (i.e., information revelation). We allow the sequencing to be endogenously determined through firms’ profit-optimizing decisions, under two 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 A as: SF∗ = 1 − + − qA 4b [ 2cA 2cB E B (cA)] ∗ (8) SL = 1 − + qB 2b [ 2cB E B (cA)] The corresponding equilibrium net present values can be derived as follows: SF 1 2 V = [ − 2cA + 2cB − E B (cA)] − I A 16rb (9) SL = 1 − 2 + 1 − + 2 − VB 4b ( cB ) 8rb[ 2cB E B (cA)] I 652 Strategic Decisions of New Technology Adoption

SL SF where Vi and Vi represent the value for the Stackelberg leader (SL) and Stackelberg follower (SF), respectively. The results in and constitute a Bayesian Nash equilibrium, because each ﬁrm’s choice is the best response to the other ﬁrm’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 opportunity to infer the leader’s private information through revealed actions. More ∗ ∗ specifically, firm B would observe firm A’s quantity decisions, q A(cH)orq A(cL), and infer firm A’s costs, cH or cL, correspondingly. This relationship is based on the 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 to estimate c. As a consequence, the impact of the information asymmetry may be mitigated. In our study, we assume that firms make quantity decisions in order to maximize their expected profits, rather than to mislead competitors. On the other hand, it is possible that firms may have incentives to signal “low cost” even when their true costs are high. Signaling sometimes does happen, but this is limited, at least to some degree, by the availability of objective information (e.g., financial statements). Further complications of signaling are out of the scope of this model. See Cho and Kreps (1987) and Fudenberg and Tirole (1991) for discussions of signaling games. Upon observing firm A’s quantity and inferring its private information, firm B chooses its own quantity to maximize its expected profit. The net present values at equilibrium are derived in Appendix A as follows: SL 1 2 1 2 V = ( − cA) + ( − 2cA + cB ) − I A 4b 8rb (10) SF = 1 − + 2 − VB 16rb( 3cB 2cA) I 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 these results to analyze the technology adoption decisions in the first stage. Both firms A and B are considering whether to adopt the new technology in anticipation of the 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 combination of firms’ strategies. Namely, (I, D) means that firm A invests and firm B defers. Of particular interest are the leader-follower sequences under which firms adopt the new 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 a profit even though they have to split the market. Thus, everyone invests, resulting in the (I, I) equilibrium. In the second region, firm B cannot be profitable if both firms invest. 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 is further lower such that the market may accommodate only one firm, then if both invest, they will end up losing, but either one of them is profitable if only one firm invests 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.” This result is summarized below, and its derivation is provided in Appendix B.

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

(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; <¯ MONO (N, N), if demand is extremely low, min , market becomes inactive. ¯ ¯ ¯ ¯ ¯ MONO where the thresholds, H , L , L2, min, and min in descending order, are derived in Appendix B. In particular, 1 rbI ¯ = max [3c − 2c + E (c )] + 3 , 2c H 2 A B B A 1 + r B rbI −E (c ) + 3 , ¯ . (11) B A 1 + r 2 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 at equilibrium for who will be the leader and who will be the follower in adopting the new technology. The sequential pattern here conveys clear strategic advantage, as the Stackelberg leader makes greater profit than the follower. To see if these conditions hold with reasonable parameter values, we simulated them under various combinations of the parameters and found these conditions can hold true with reasonable parameter values. The intuition for these equilibria lies in the understanding that firms need to balance the tradeoff between the payoff benefits of being a leader and the informational benefits of being a follower (i.e., competing for leadership versus waiting for information). When the demand is high enough, it becomes clear that the payoff benefits from investing immediately will outweigh any informational benefits from waiting; so both firms invest. In contrast, if the demand is so low that even the extra reward of being a leader cannot compensate for the investment cost required to adopt the technology, then both will defer. In the second region, however, the tradeoff is subtler. Firm A captures more profits by being the leader. On the other hand, firm B, having inferior information, would benefit by waiting and learning the leader’s (superior) private information. For firm B, the informational benefits 654 Strategic Decisions of New Technology Adoption 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 structure. A low-cost firm A (i.e., cA = cL) would always want to invest. A high-cost firm A (i.e., cA = cH) would defer its investment if demand is low. This result leads to a separating equilibrium in the sense that firm A defers only when it is a high-cost firm. 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 still cannot 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 as this 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 the two firms. From (B7) in Appendix B, 1 7 1 E V NS − E V SF = + ( − c )2 − σ 2. (12) B B 9b 144br B 4br c

σ 2 It shows that if is sufficiently large or c is sufficiently small, firm B should σ 2 invest in the first period, leading to an (I, I) equilibrium. On the other hand, if c 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 by information asymmetry rather than cost asymmetry. In this case, informational advantage may transfer to strategic leadership, even without any other advantages. σ 2 We may use c to represent the degree of information asymmetry, whereas smaller variance means less asymmetry of information. Then, lower variance makes firm B to be more likely to invest in the first period. The key point is that, when information asymmetry is not severe, it is less useful for firm B to defer the investment in order to learn firm A’s cost.

The Effect of Demand Uncertainty In the above section, we assumed that market demand was constant. Now we relax this assumption by allowing to change during the first and the second period. The demand is modeled as a simple stochastic binomial variable. More precisely, 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 and d < 1), as illustrated in Figure 3. We use ˜ to represent the stochastic demand 2 with expected value, E˜ , and variance, var(˜ ) = σ. Both can be computed from known parameters, , u, d, and p. 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 new technology can be reasonably computed. Zhu and Weyant 655

Figure 3: Demand uncertainty.

u Θ up p Θ 1-p

down d Θ

PePeriod 1 Period 2

As shown in Appendix C, the net present value expressions in (C1)∼(C4) con- σ 2 1 + r σ 2 1 σ 2 1 σ 2 1 σ 2 tain extra terms associated with , namely, 9rb , 16rb , 8rb , and 9rb . No- 2 tice that these extra σ terms are due to the stochastic nature of the demand. If we set 2 σ = 0, we return to the case discussed in the previous section. It can be shown that the results in the previous section still holds. Thus the introduction of stochastic demand does not qualitatively alter the firms’ strategies. Moreover, because of the rel- σ 2 1 + r σ 2 > 1 σ 2 1 σ 2 > 1 σ 2 ative strength of the extra terms, that is, 9rb 16rb and 8rb 9rb , it reinforces the incentives for firm A to invest early. Thus, compared to the case of constant demand, firm A has an even stronger incentive to invest in the first period. For firm B, it can be shown 1 V NS − V SF = [ − 2c + E (c )]2 B B 9b B B A 1 + [7E˜ − 17c + 10E (c )][E˜ + c − 2E (c )] 144rb B B A B B A

7 2 1 2 + σ − σ 144rb 4rb c All other terms are positive, hence its sign depends on the sign of

7 2 1 2 = σ − σ , (13) 144rb 4rb c = σ 2 ˜ = σ 2 where two variance terms, var(cA) c and var( ) account for the effects of the two stochastic variables, because the model now has two types of uncertainties—demand uncertainty and cost uncertainty. This suggests that whether the equilibrium is (I, I) or (I, D) is determined by the relative degree of demand uncertainty and cost uncertainty. The former works to the advantage to firm B (as it deters its rival from being aggressive), but the latter works as the informational disadvantage to firm B. − 1 σ 2 Severe information asymmetry, as represented by 4rb c , may offset the NS − SF positive terms in VB VB . In other words, if firm A’s cost appears widely uncertain to firm B, firm B would defer its investment. However, compared to the case of constant demand, firm B now has stronger inventive to invest early, 656 Strategic Decisions of New Technology Adoption

7 σ 2 as represented by the extra positive term, 144rb . Hence, it becomes more likely that the equilibrium would be (I, I) rather than (I, D). As proved analytically in Appendix C, we have the following result:

Proposition 2 (The effect of demand uncertainty): The introduction of stochastic demand reinforces the beneﬁts for ﬁrms A and B to invest early. Consequently, 2 demand uncertainty, σ , makes equilibrium (I, I) more likely and (I, D) less likely.

This result may sound counterintuitive and different from the established decision theory about uncertainty. In the presence of uncertainty, a decision maker would normally defer her decision in order to learn more information to resolve the 2 uncertainty. But, our model shows that, if σ is sufficiently large, firms will find it optimal to invest early. The rationale can be explained as follows. Demand uncertainty, unlike cost uncertainty, is a common uncertainty to both firms (while cost uncertainty is a private one). This common uncertainty gives firm B a fair chance to compete with firm A in a playfield that is made more even by the demand uncertainty. We mentioned earlier the real options view on uncertainty. Because firms can adjust their production quantity in the second period (after they have adopted the technology), they essentially hold an option of scaling up or down the quantity depending on whether the demand goes up or down in the second period. The real options literature shows that greater uncertainty actually increases the value of the option (Dixit & Pindyck, 1994; Zhu, 1999; Zhu & Weyant, 2003). Our result is consistent with this view:

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 might be useful now to compare the equilibria under asymmetric information to those under full information, so that we can better gauge the effects of information asymmetry.

Adoption Patterns Comparing the adoption patterns under asymmetric information and those under full information, we can see the effect of different information structures. Under symmetric information, the equilibrium of the adoption game exhibited a simultaneous adoption pattern: both ﬁrms will either adopt the technology simultaneously or the technology market remains inactive until the product market develops more favorably. Under asymmetric information, we found that the adoption pattern can be very different from that under full information. The adoption pattern becomes sequential (for a range of parameter values), as shown in Proposi- tion 1. This suggests that leadership may endogenously emerge from information asymmetry. Zhu and Weyant 657

For ﬁrm B, the thresholds of adopting the technology with full information would be:  ¯ NS = , = − + rbI B (cA cL FI) 2cB cL 3 1 + r , (14) ¯ NS = , = − + rbI B (cA cH FI) 2cB cH 3 1 + r

With asymmetric information, the corresponding threshold from Proposi- tion 1 becomes: ¯ NS ξ, = − − ξ − + rbI , B ( AI) 2cB cL (cH cL ) 3 1 + r (15) where FI denotes “Full Information” and AI “Asymmetric Information.” ¯ NS | = , B (cA cH FI) stands for the adoption threshold conditional on firm B having ξ = ¯ NS | ξ, full information and believing firm A’s cost is cH ( 1). Similarly, B ( AI) represents the adoption threshold conditional on firm B’s belief that cA = cH with probability ξ ∈ (0, 1). From this we have ∂¯ NS (ξ, AI) B =−c − c < . ∂ξ ( H L ) 0 (16) ¯ NS | ξ, ξ Thus B ( AI) is a decreasing function of , implying that firm B would invest at a lower threshold (thus more aggressively) if it has a stronger belief that its competitor is a high-cost player. This aggressive behavior will make simultaneous adoption, (I, I), more likely. Notice that (14) can be obtained from (15) by setting ξ = 0 and ξ = 1, ¯ NS | = , ¯ NS | = , respectively, making B (cA cH FI) and B (cA cL FI) two extreme ¯ NS | ξ, values of B ( AI). Thus, the full-information thresholds are special cases of the asymmetric-information threshold. It can be verified that ¯ NS = , < ¯ NS ξ, < ¯ NS = , . B (cA cH FI) B ( AI) B (cA cL FI) ¯ NS | ξ, That is, the adoption threshold under asymmetric information, B ( AI), is ¯ NS | = , ¯ NS | = , greater than B (cA cH FI) but lower than B (cA cL FI). This occurs because firm A not only tailors its adoption strategy to its own cost but also responds to 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 waits longer because it knows that firm B will invest at a lower threshold than firm B would have if it had full information about firm A’s low cost. To sum up, information asymmetry is often combined with cost asymmetry in many realistic settings. Allowing these two types of asymmetry to coexist makes the model more realistic. Our analysis showed interesting dynamics by modeling this combination, where pure information asymmetry and pure cost asymmetry can be considered special cases of the model. Clearly, informational advantage will always amplify cost advantage. More interestingly, informational advantage tends to mitigate the cost disadvantage in a subtle way that depends on the relative degree of information asymmetry. In addition, the coupling of information asymmetry and cost asymmetry leads to another interesting dynamic to which we now turn. 658 Strategic Decisions of New Technology Adoption

Having Better Information Could Hurt You We have seen above that asymmetric information about a rival’s cost introduces different strategic dynamics to the technology adoption game. There is one more question that our model might be useful in answering; namely, is more information always better? Under symmetric information, as documented in the existing literature on value 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 have asymmetric information in strategic games, especially when rivals have asymmetric information about a private parameter such as the postadoption cost that is directly linked to their incentives to adopt the technology. We examine this question in the following context: Firm A knows its true cost is low, that is, cA = cL, while firm B only 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 firm A’s cost. Both firms take this into consideration in making adoption decisions. Our analysis reveals a surprising result:

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

As shown in Appendix D, a lower ξ (corresponding to better information) may cause two types of effects on firm B’s profits. (i) It may cause a shift of equilibrium in 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 , hence causing a shift of equilibrium from (I, I)to(I, D), thus reducing firm B’s profitable region, as illustrated in Figure 4. (ii) A lower ξ may lead to lower incremental ∂ NS/∂ξ > profits even when it does not cause the equilibrium to shift, that is, VB 0. Both these effects are negative on firm B’s profit.

Figure 4: Better information may cause an equilibrium shift.

ξ (D(D, D) (I, D) (I, I) Θ Θ*

benefit firm A, hurt firm B

Firm B’s better information, represented by a lower ξ, may cause a shift of equilibrium in a direction that hurts firm B. Because the threshold ∗ is a decreasing function of ξ,alower ξ increases the threshold ∗, hence causing the equilibrium region (I, I) to shrink, which in turn reduces firm B’s profit. Zhu and Weyant 659

The following intuition may help explain the rationale. If ξ is low, meaning that firm B has fairly accurate information about firm A’s cost, this leads firm B to behave conservatively in adopting the technology because it believes its competitor is strong (i.e., has low cost). On the other hand, if ξ is high, firm B confidently believes that firm A is a weak rival (with high cost). This more “optimistic,” albeit less accurate, belief about its competitor’s cost leads firm B to behave aggressively in adopting the technology, which results in higher profit for firm B. In terms of the example we mentioned in the Introduction, we could consider Ford as firm A and GM as firm B. Prior experience with EDI gives Ford superior information 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 after implementing the e-procurement system. In this case, if GM believes Ford’snew production cost is indeed low, it will behave more conservatively by producing and selling fewer cars to the automobile market (based on the rational assumptions in a Cournot game). Ford knows this and thus behaves more aggressively. This will lead to a lower profit, ceteris paribus, for GM than if it believes Ford’s cost might 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 lower equilibrium profit for GM. Lower cost means a stronger competitor. When your competitor is strong, you would rather not know this. The fundamental point is that information asymmetry has changed the behavior of both competitors under these circumstances. Thus, having better information, or more precisely, having it known to the rival that one has better information, may actually hurt a firm! The observation that firm B does worse when it has better information illustrates an important difference between single- and multi-agent decision problems.

Corollary 3 In conventional decision theory, having more information can never make the decision maker worse off. However, in a multi-agent game-theoretic setting, having more 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 technology adoption decisions beyond the full-information models typically considered in the literature. We have found that adoption strategies under asymmetric information can be very different from those under full information. For example, equilibrium adoption patterns become sequential, which indicates that leadership may endogenously emerge from information asymmetry, even when it is balanced by conflicting forces such as a cost disadvantage. In contrast to conventional wis- dom, our model shows that common market uncertainty may actually induce firms to act more aggressively under certain conditions. Our model also demonstrates how information asymmetry on private costs would change the strategic behavior of both competitors, which leads to a surprising, but interesting result; namely, having better information could actually hurt a firm. A departure from conventional 660 Strategic Decisions of New Technology Adoption decision theory, these results illustrate that different decision dynamics may arise in a game-theoretic setting with asymmetric information. In light of the significant amount of uncertainty that companies typically encounter about the outcome of technology implementation in real business environments, the asymmetric information setting appears to be more realistic than the typical full-information assumption. In today’s technology-based companies, innovations develop rapidly and managers constantly face adoption decisions. The ultimate goal of studying the technology-adoption game is to provide an underlying theory from which one may better understand strategic adoption decisions. A single model cannot answer all the important questions, but we hope that the present model has generated some new insights into the tradeoffs that shape technology leadership under asymmetric information. This seems to be particularly relevant to many situations involving information technology where adoption decisions are frequently driven by competitive considerations. We hope this will motivate other researchers to engage in further studies on these issues. Indeed, we see this paper as an early attempt to understand the link between technology adoption and asymmetric information. It leaves many issues open for further study. For example, the current model can be extended to study potential signaling strategies and gaming behavior—how firms with superior information may attempt to mislead competitors and alter the information structure. Also, technology investments may produce multiple benefits beyond the cost dimension that is considered in the current model, such as higher quality, faster delivery, and better customer services. A more general reward function may be required to incorporate these factors. The current study provides a base on which more sophisticated models can be built. We keenly anticipate others’ ideas and efforts to pursue related research. [Received: August 2002. Accepted: August 2003.]

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APPENDIX A Derivation of Equilibrium Quantities and Profits Simultaneous Decisions When firms choose quantities simultaneously, they engage in a Cournot game. We solve for the optimal quantities in the Cournot-Nash equilibrium by following the standard 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 maximize its profit:

Max πA(qA, qB | cH ) = Max [P(,qA, qB ) − cH ]qA. (A1) qA qA ∗ Similarly, it will choose q A(cL) if its cost is cL:

Max πA(qA, qB | cL ) = Max [P(,qA, qB ) − cL ]qA. (A2) qA qA where π i is firm i’s profit, and P(, qA, qB) = − b(qA + qB)asdefined in the section on model setup. Firm B, however, does not know firm A’s true cost. It has to optimize its expected profit under this incomplete information. Firm B believes that firm A’s cost is high with probability ξ and low with probability (1 − ξ), as defined in the section on model setup. Absent any further information, it thus should ∗ ξ anticipate that firm A’s quantity choice would be q A(cH) with probability , and ∗ − ξ q A(cL) with probability (1 ), respectively. Mathematically, firm B’s decision is ∗ to choose q B so as to maximize its expected profit, that is,

Max πB (qA, qB | ξ) qB

= Max{ξ[P(,qA(cH ), qB ) − cB ]qB + (1 − ξ)[P(,qA(cL ), qB ) − cB ]qB }. qB (A3) By following the standard Cournot approach (Varian, 1992, pp. 285–291; Rasmusen, 1989, pp. 309–313), the simultaneous solution of the first-order conditions of (A1)∼(A3) yields the equilibrium quantities: ∗ 1 1 q = − (3cA − 2cB + E B (cA)) A 3b 2 (A4) ∗ = 1 − + qB 3b [ 2cB E B (cA)] Zhu and Weyant 663 and the corresponding profits: ∗ 1 1 2 ∗ 2 π = − (3cA − 2cB + E B (cA)) = b q A 9b 2 A (A5) π ∗ = 1 − + 2 = ∗ 2 B 9b [ 2cB E B (cA)] b qB where cA ={cL , cH }, EB(cA) = ξcH + (1 − ξ)cL is the expected cost of firm A ∗ π ∗ (from firm B’s perspective); qi (and i ) denotes optimal quantity (profit) for firm i at equilibrium. Checking the second-order conditions confirms that these quantities indeed maximize the expected profits. The profits in (A5) represent the cash flows generated by the new technology in each production period. Suppose that the discount rate is r, the present value of investing in the technology can be calculated by summing up the profitofthe initial period and the discounted cash flows of all future periods: V NS = 1 + r − 1 (3c − 2c + E (c )) 2 − I A 9br 2 A B B A (A6) NS = 1 + r − + 2 − VB 9rb [ 2cB E B (cA)] I

NS where Vi 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 generate cash flows for n periods in the production stage. Hence the present value of the π π = n i − →∞ = i − future cash flows is V i=1 (1 + r)i I .Ifn , then V r I . Hence, we have the results in (A6). This assumption, albeit simplistic, avoids the complication of 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 sequential game. There are two possible sequences as speciﬁed below.

Sequence 1: The less-informed firm (B) moves first and the more-informed firm (A) follows Since firmBmovesfirst, it is a tentative monopoly in the first period. Then firm A invests in the technology and joins the market as a Stackelberg follower. Using the backward 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’s decision in the following manner. Assuming the leader (firm B) has already decided ∗ qB, the follower (firm A) will choose q A to maximize its profit conditional on its cost function:   Max πA(qA, qB | cH ) = Max [P(,qA(cH ), qB (qA)) − cH ]qA(cH ) qA(cH ) qA(cH )  (A7) Max πA(qA, qB | cL ) = Max[P(,qA(cL ), qB (qA), ) − cL ]qA(cL ) qA(cL ) qA(cL ) 664 Strategic Decisions of New Technology Adoption

∗ Anticipating ﬁrm A’s above move, the leader’s decision is to choose q B to maximize its expected payoff, that is,

Max πB (qA, qB | ξ) q B = ξ , ∗ , − + − ξ , ∗ , − . Max P qA(cH ) qB cB qB (1 ) P qA(cL ) qB cB qB qB (A8) Jointly solving (A7)∼(A8) yields the equilibrium quantities: SF∗ = 1 − + − qA 4b [ 2cA 2cB E B (cA)] ∗ (A9) SL = 1 − + qB 2b [ 2cB E B (cA)] and the corresponding equilibrium proﬁts: ∗ 1 2 SF∗ 2 π = [ − 2cA + 2cB − E B (cA)] = b q A 16b A (A10) π ∗ = 1 − + 2 = SL∗ 2 B 8b [ 2cB E B (cA)] b qB

Similar to the first appendix section, the present value of investing in the technology can be computed by summing up discounted future cash flows: 1 SF = − + − 2 − VA [ 2cA 2cB E B (cA)] I (A11) 16rb Stackelberg follower profit

1 1 SL = − 2 + − + 2 − VB ( cB ) [ 2cB E B (cA)] I (A12) 4b 8rb Monopoly proﬁt Stackelberg leader proﬁt

SL SF where Vi and Vi represent the value for the Stackelberg leader (SL) and Stackel- 1 − 2 berg follower (SF), respectively; the term, 4b ( cB ) , represents the monopoly proﬁt 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 the discount rate so as to avoid incentives from possible change of investment cost. When discounted back to the present value, future investment cost remains the same in terms of present value.

Sequence 2: The more-informed firm (A) moves first and the less-informed firm (B) follows Upon observing firm A’s quantity and inferring its private cost information, firm B chooses its own quantity to maximize its expected profit. Firm A’s move could reveal to firm B two possibilities: firm A’s cost is high (cA = cH)orlow(cA = cL). Conditional on cA = cH, firm B’s decision is: π ∗ , = = , ∗ , − . Max B qA(cH ) qB cA cH Max P qA(cH ) qB cB qB (A13) qB qB

Similarly, conditional on cA = cL, ﬁrm B’s decision would be: π ∗ , = = , ∗ , − . Max B qA(cL ) qB cA cL Max P qA(cL ) qB cB qB (A14) qB qB Zhu and Weyant 665

∗ Anticipating ﬁrm B’s above responses, ﬁrm A chooses q A(cH) when its true cost is cH, that is, π , ∗ = = , , ∗ − , Max A qA(cH ) qB cA cH Max P qA(cH ) qB (qA) cH qA(cH ) qA(cH ) qA(cH ) (A15)

∗ and q A(cL) when its true cost is cL, that is, π , ∗ | = = , , ∗ − . Max A qA(cL ) qB cA cL Max P qA(cL ) qB (qA) cL qA(cL ) qA(cL ) qA(cL ) (A16)

Solving these optimization problems jointly yields the following equilibrium quantities: SL∗ = 1 − + qA 2b ( 2cA cB ) ∗ (A17) SF = 1 − + qB 4b ( 3cB 2cA)

The corresponding equilibrium proﬁts are, respectively, ∗ 1 2 π = ( − 2cA + cB ) A 8b (A18) π ∗ = 1 − + 2 B 16b ( 3cB 2cA)

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

1 SL = − 2 + 1 − + 2 − VA ( cA) ( 2cA cB ) I (A19) 4b 8rb Stackelberg leader proﬁt Monopoly proﬁt

1 SF = − + 2 − VB ( 3cB 2cA) I (A20) 16rb Stackelberg follower proﬁt

Notice that cA is known this time, hence cA rather than E(cA) is contained in the solution. Finally, both firm A and firm B could defer the investment to the second period. This scenario is similar to the Nash-Cournot equilibrium in the first appendix section (except they missed the first-period profit): V NS2 = 1 − 1 (3c − 2c + E (c )) 2 − I A 9rb 2 A B B A (A21) NS2 = 1 − + 2 − VB 9rb[ 2cB E B (cA)] I

NS2 where V i denotes the present value of ﬁrm i under Nash-Cournot equilibrium when both ﬁrms invest in the second period (NS2). 666 Strategic Decisions of New Technology Adoption

APPENDIX B Derivation of Adoption Equilibria under Asymmetric Information (Proposition 1) The Nash-Cournot equilibrium is achieved by interrelated best responses to each other’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’s strategy is given. Making use of the subgame equilibrium results in Appendix A, we can compute firm A’s payoffs as follows under four different strategy combinations corresponding to the four branches in Figure 2: | = NS = 1 + r − 1 − + 2 (i) VA(A invests B invests) VA 9rb [ 2 (3cA 2cB E B (cA))] − = (1 + r)b NS∗ 2 − I r (qA ) I ; | = SF = 1 − + − 2 − (ii) VA(A defers B invests) VA 16rb( 2cA 2cB E B (cA)) = b SF∗ 2 − I r (qA ) I ; | = SL = 1 − 2 + 1 − + 2 (iii) VA(A invests B defers) VA 4b ( cA) 8rb( 2cA cB ) − = 1 − 2 + b SL∗ 2 − I 4b ( cA) 2r (qA ) I ; | = NS2 = 1 − 1 − + 2 (iv) VA(A defers B defers) VA 9rb[ 2 (3cA 2cB E B (cA))] − = b NS∗ 2 − I r (qA ) I . where the superscripts NS, SL, SF, and NS2 denote the sequence of the game as Nash, Stackelberg leader, Stackelberg follower, and deferred Nash equilibrium. First, comparing (i) and (ii) yields NS − SF > , VA VA 0 (B1) which means that VA(A invests | B invests) > VA(A defers | B invests). Given these two options, it is a dominant strategy for firm A to invest in the first period rather than defer to the second period. Next, to compare (iii) and (iv), we have: 2 1 b 1 ∗ ∗ 1 ∗ ∗ SL − NS2 = − + √ SL + NS √ SL − NS VA VA cA qA qA qA qA (B2) 4b r 2 2 ∗ ∗ Its sign depends on the sign of ( √1 q SL − q NS ), as the other terms are positive. 2 A A √ √ √ 1 ∗ ∗ 3 − 2 2 √ SL − NS = √ − + + + + qA qA 6 3 2 cA cB 4 3 2 E B (cA) 2 6 2b (B3)

If cA = cL, it can be shown: SL − NS2 > , = . VA VA 0 if cA cL (B4) which means that, if cA = cL, ﬁrm A would rather like to be a Stackelberg leader than split the market with ﬁrm B. Zhu and Weyant 667

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

SL − NS2 > , ≥ ¯ = VA VA 0 if b and cA cH (B5) where √ √ ¯ b = 6 + 3 2 cH − cB − 4 + 3 2 E B (cA). (B6)

Firm A would invest when demand is high enough (i.e., ≥ ¯ b). <¯ SL − NS2 < However, if b, VA V A 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 A would always want to invest. Together these results lead to a separating equilibrium in 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 moving after 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, firm A cannot hide its cost by deferring, as this action itself would reveal information to its competitor. By deferring, firm A would still reveal its cost, but it gets lower profit than being a Stackelberg leader. Knowing this tradeoff, firm A would invest in the first period (as long as demand is above a certain threshold, which will be specified later).

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

1 + r (i) E [V (B invests | A invests)] = E V NS = [ − 2c + E (c )]2 − I B B B 9rb B B A (1 + r)b ∗ = q NS 2 − I, r B 1 (ii) E [V (B defers | A invests)] = E V SF = [ − 3c + 2E (c )]2 B B B 16rb B B A 1 b ∗ 1 + σ 2 − I = E q SF 2 + σ 2 − I 4rb c r B B 4rb c

σ 2 = where term c 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:

1 E V NS − E V SF = [ − 2c + E (c )]2 B B 9b B B A 1 + [7 − 17c + 10E (c )] 144rb B B A 1 × [ − 2E (c ) + c ] − σ 2 (B7) B A B 4rb c 668 Strategic Decisions of New Technology Adoption

NS − SF = Solving this equation, E(VB ) E(VB ) 0, yields two roots, but only one of them is meaningful: 1 ¯ = (5 + 32r)c + 2(1 − 8r)E (c ) 2 7 + 16r B B A 2 2 + 6 4(1 + r)(cB − E B (cA)) + (7 + 16r)ξ(1 − ξ)(cH − cL ) (B8) Because (B7) is a convex function, then NS − SF ≥ , ≥ ¯ . E VB E VB 0 if 2 (B9)

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

(A) If demand is sufﬁciently high, Θ ≥ Θ¯ H, the equilibrium is (I, I) An (I, I) equilibrium will require that all of the following conditions be met: 1 rbI V NS > 0 ⇒ >¯ NS = [3c − 2c + E (c )] + 3 A A 2 A B B A 1 + r rbI V NS > 0 ⇒ >¯ NS = 2c − E (c ) + 3 B B B B A 1 + r

NS − SF > VA VA 0 (satisﬁed as proved in (B1))

NS − SF > ⇒ >¯ VB VB 0 2 (from (B9)) ¯ NS where i denotes the threshold of demand that will make ﬁrm i’s value positive under Nash-Cournot equilibrium (NS). Similar notations are used below where the superscript stands for the sequence of the game, that is, NS, SL, SF, NS2, and MONO (for monopoly). For notational convenience, deﬁne ¯ = ¯ NS, ¯ NS, ¯ H max A B 2 1 rbI rbI = max [3c − 2c + E (c )] + 3 , 2c − E (c ) + 3 , ¯ 2 A B B A 1 + r B B A 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, Θ¯ L ≤ Θ < Θ¯ H, the equilibrium is (I, D)

If demand is lower than ¯ H , an (I, D) equilibrium may result if the following conditions are met: SL > ⇒ >¯ SL VA 0 A 1 = 2(1 + r)c − c + 8br I (1 + 2r) − 2r(c − c )2 1 + 2r A B B A √ SF > ⇒ >¯ SF = − + VB 0 B 3cB 2cA 4 rbI

SL − NS2 > = , = ≥ ¯ VA VA 0 (satisﬁed if cA cL or if cA cH and b)

SF − NS ≥ ⇒ ≤ ¯ VB VB 0 2 from (B9) Define ¯ = ¯ SL, ¯ SF, ¯ . L max A B b (B11) In this region, firm B cannot be profitable if both firms invest. Thus B will not invest if B believes that A is going to invest. Since firm B cannot make a profitin this region unless firm A stays out, but firm A is not going to stay out, firm B will not invest. Because firm A’s threshold is lower than firm B’s, firm A’s incentive to invest early is stronger than firm B’s. Thus it is impossible for firm A to wait and allow firmBtoinvestfirst and become a leader.

(C) If demand is low, Θ¯ L2 ≤ Θ < Θ¯ L, the equilibrium may be (D, D) Based on the above analysis, ﬁrm A would rather invest in the ﬁrst period than defer, if cA = cL or if cA = cH and ≥ ¯ b. This makes the (D, D) equilibrium infeasible if cA = cL. Only when cA = cH, a (D, D) equilibrium is possible, which would require the following conditions: √ NS2 > ⇒ >¯ NS2 = 1 − + + VA 0 A 2 (3cA 2cB E B (cA)) 3 rbI √ NS2 > ⇒ >¯ NS2 = − + VB 0 B 2cB E B (cA) 3 rbI

SL − NS2 < ⇒ <¯ VA VA 0 b Deﬁne ¯ = ¯ NS2, ¯ NS2 L2 max A B (B12)

(D) If demand is very low, Θ¯ min ≤ Θ < Θ¯ L2, the equilibrium may be (I, N) or (N, I) NS2 < NS2 < MONO > MONO > If demand is further lower, then V A 0orV B 0, but V A 0 and VB 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, either one of them is profitable. There are two Nash equilibria in this scenario: (I, N) and MONO = > MONO ≤ (N, I), where N denotes “Not invest.” If V A (cA cL) 0 and VB 0, then 670 Strategic Decisions of New Technology Adoption

firm A invests and enjoys being a monopoly in the market because of its low cost. MONO = < This results in an (I, N) equilibrium. On the other hand, if V A (cA cH) 0 MONO > but VB 0, then firm B invests as a monopoly, leading to a (N, I) equilibrium. Define brI brI ¯ = min ¯ MONO, ¯ MONO = min c + 2 , c + 2 (B13) min A B A 1 + r B 1 + r <¯ MONO If min , 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, 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 and d < 1), as illustrated in Figure 3. It can be shown√ that u and√d are related to σ of . The relationship is determined 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 new technology can be reasonably computed. Following a similar structure to Appendix B, we analyze firm A’s strategy first, then firm B’s, even though the Nash-Cournot equilibrium is really achieved by 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 four scenarios: 1 1 2 (i) E V NS = − (3c − 2c + E (c )) A 9b 2 A B B A (C1) 2 1 1 1 2 + E˜ − (3c − 2c + E (c )) + σ − I 9rb 2 A B B A 9rb SF 1 2 1 2 (ii) E V = (E˜ − [2c − 2c + E (c )]) + σ − I (C2) A 16rb A B B A 16rb SL 1 2 1 2 1 2 (iii) E V = ( − c ) + (E˜ − 2c + c ) + σ − I (C3) A 4b A 8rb A B 8rb 2 NS2 1 1 1 2 (iv) E V = E˜ − (3c − 2c + E (c )) + σ − I (C4) A 9rb 2 A B B A 9rb where ˜ represents the stochastic demand with expected value, E˜ , and 2 variance,var(˜ ) = σ. Both can be computed from known parameters, , u, d, 2 and p. Notice that the extra term σ in each equation above is due to the stochastic Zhu and Weyant 671

2 nature of the demand. If we set σ = 0, the above four equations become the same as those in Appendix B. 1 + r σ 2 > 1 σ 2 1 σ 2 > 1 σ 2 Because 9rb 16rb and 8rb 9rb , it can be shown the results in Appendix B still holds: E V NS > E V SF A A (C5) SL > NS2 , = E VA E VA if cA cL Thus the introduction of stochastic demand does not qualitatively alter the firms’ 2 strategies. In fact, because of the relative strength of the extra σ terms, i.e., 1 + r σ 2 > 1 σ 2 1 σ 2 > 1 σ 2 9rb 16rb and 8rb 9rb ,itreinforces the benefits for firmAtoinvest early. Thus, compared to the situation in Appendix B, firm A has an even stronger incentive to invest in the first period.

Firm B’s Strategy Having analyzed firm A’s strategies, we now consider firm B’s payoffs. Given the above result, firm B only needs to compare the values of the following two options: 1 1 (i) E V NS = [ − 2c + E (c )]2 + [E˜ − 2c + E (c )]2 B 9b B B A 9rb B B A

1 2 + σ − I 9rb

SF 1 2 1 2 1 2 (ii) E V = [E˜ − 3c + 2E (c )] + σ + σ − I B 16rb B B A 16rb 4rb c = σ 2 ˜ = σ 2 where two variance terms, var(cA) c and var( ) account for the effects of the two stochastic variables, because ﬁrm B now faces two types of uncertainties— demand uncertainty and cost uncertainty. To compare (i) and (ii), we have 1 E V NS − E V SF = [ − 2c + E (c )]2 B B 9b B B A 1 + [7E˜ − 17c + 10E (c )] 144rb B B A

7 2 1 2 × [E˜ + c − 2E (c )] + σ − σ (C6) B B A 144rb 4rb c All other terms are positive, hence its sign depends on the sign of

7 2 1 2 = σ − σ , (C7) 144rb 4rb c namely, the relative degree of demand uncertainty and cost uncertainty. The former works to the advantage to firm B (as it deters its rival from being aggressive), but the latter works as the informational disadvantage to firm B. − 1 σ 2 Severe information asymmetry, as represented by 4rb c , may offset the positive terms in (C6). In other words, if firm A’s cost appears widely uncertain to firm B, firm B would defer its investment. However, compared to the case of 672 Strategic Decisions of New Technology Adoption constant demand as analyzed in Appendix B, firm B now has stronger inventive to 7 σ 2 invest early, as represented by the extra positive term, 144rb . 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 not severe, 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 positive 7 σ 2 term 144rb , which may make (C6) to be positive even when (B7) is negative. Thus, the demand uncertainty does not qualitatively change the dominant strategy of 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 effects on firm B’s profits, as illustrated in Figure 4. (i) It may cause a shift of equilibrium in a direction that hurts firm B; and (ii) it may lead to lower incremental profits even when it does not cause the equilibrium to shift. Below we show these two effects respectively. First we consider how the change of ξ may affect firm B’s investment decision (i.e., equilibrium shift). Next, we consider the situation that if firm B has already decided to make investment in the first period, how better information affects its payoff (i.e., incremental change). (i) Equilibrium shift: From Proposition 1, the threshold for simultaneous investment is ¯ H , which is defined in (B10). If ≥ ¯ H , firm A and firm B will = ¯ = {¯ NS, ¯ } prefer to invest, leading to an (I, I) equilibrium. If cA cL, H max B 2 , ¯ NS ¯ where B and 2 are determined in Appendix B. By taking first derivative with respect to ξ, it can be shown:

∂¯ NS B =−c − c < ∂ξ ( H L ) 0 (D1)

∂¯ 1 2 = (c − c ) ∂ξ 7 + 16r H L 3[8(1 + r)c + 3(2 + 8r)E (c ) − (7 + 16r)(c + c )] × 2(1 − 8r) − B B A H L < 0 2 2 4(1 + r)(cB − E B (cA)) + (7 + 16r)ξ(1 − ξ)(cH − cL ) (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 a smaller (I, I) region, which eventually reduces firm B’s profit. As illustrated in Figure 4, a lower ξ increases the upper threshold ¯ H (but it has no effect on the lower 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 in Appendix B, region (I, I) is the best region in which ﬁrm B’s proﬁt will be the highest. Moreover, as shown in Appendix B,

1 + r (1 + r)b ∗ V NS = [ − 2c + E (c )]2 − I = q NS 2 − I. B 9rb B B A r B Taking ﬁrst derivative with respect to ξ,weget ∂V NS 2(1 + r)[ − 2c + ξc + (1 − ξ)c ] B = B H L (c − c ) ∂ξ 9rb H L

2(1 + r) ∗ = q NS (c − c ) > 0 (D3) 3r B H L 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, that is, 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 2 = σ 2 c Variance of cost, var(c) 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). ∗ qi Optimal quantity at equilibrium. Demand intercept. ˜ Stochastic demand. 2 2 σ Variance of stochastic demand, var(˜ ) = σ. 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. NS Vi Present value of future profit streams, where the subscript denotes the firms and the superscript represents the equilibrium paths, where NS, SL, SF, NS2, MONO denote Nash, Stackelberg leader, Stackelberg follower, deferred Nash equilibrium, and monopoly, respectively. 674 Strategic Decisions of New Technology Adoption

¯ NS i Threshold of demand that makes firm i’s value positive under Nash-Cournot equilibrium (NS). Similar notations are used for other equilibria where the superscripts SL, SF, NS2, MONO denote Stackelberg leader, Stackelberg follower, deferred Nash equilibrium, and monopoly, respectively. (I, D) Strategy pair, meaning firm A invests (I) while firm B defers (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. ¯ NS | = , B (cA cH FI) Threshold conditional on firm B having full information and believing firm A’s cost is cH. ¯ NS | = , B (cA cL FI) Threshold conditional on firm B having full information and believing firm A’s cost is cL. ¯ NS | ξ, = B ( 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 Investment in Information Technologies: A Real-Options and Game-Theoretic Approach,” in which he pioneered an innovative approach that integrated real options and game theory for modeling investment strategies under competition. His current research focuses on strategic investment in information technologies, economics of information systems and electronic markets, economic and organizational impacts of information technology, and information transparency in supply chains. His research methodology 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 of his papers has won the Best Paper Award of the International Conference on Infor- mation Systems (ICIS), 2002. He was the recipient of the Academic Achievement Award of Stanford University, the Faculty Research Award of the University of California, and the Charles and Twyla Martin Excellence in Teaching Award. See more information at http://web.gsm.uci.edu/kzhu/.

John P. Weyant is professor of management science and engineering at Stanford University, a senior fellow in the Institute for International Studies, and director of the Energy Modeling Forum (EMF) at Stanford University. Professor Weyant earned a BS/MS in aeronautical engineering and astronautics, MS degrees in engineering management and in operations research and statistics all from Rensselaer Polytechnic 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 modeling, options, policy, and strategy. His current research focuses on economic models for strategic planning, competition, and investment in high-tech industries, and analysis of global climate change policy options. He is on the editorial boards of Integrated Assessment, Environmental Management and Policy, and The Energy Journal and a member of INFORMS, the American Economics Association, and American Finance Association.