STRATEGIC EXERCISE OF REAL OPTIONS: INVESTMENT …rady.ucsd.edu/faculty/directory/zhu/pub/docs/papers/... · 2012. 7. 5. · Strategic Exercise of Real Options: Investment Decisions

ISSN 1004-3756/03/1203/257 JOURNAL OF SYSTEMS SCIENCE AND SYSTEMS ENGINEERING CN11- 2983/N ©JSSSE 2003 Vol. 12, No. 3, pp257-278, September, 2003

STRATEGIC EXERCISE OF REAL OPTIONS:

INVESTMENT DECISIONS IN TECHNOLOGICAL SYSTEMS

Kevin ZHU John WEYANT

Graduate School of Management

University of California, Irvine, CA 92697-3125, USA [email protected]

Department of Management Science and Engineering Stanford University, Stanford, CA 94305-4026, USA

Abstract

Viewing investment projects in new technologies as real options, this paper studies the effects of endogenous competition and asymmetric information on the strategic exercise of real options. We first develop a multi-period, game-theoretic model and show how competition leads to early exercise and aggressive investment behaviors and how competition erodes option values. We then relax the typical full-information assumption found in the literature and allow information asymmetry to exist across firms. Our model shows, in contrast to the literature that payoff is independent of the ordering of exercise, that the sequential exercise of real options may generate both informational and payoff externalities. We also find some surprising but interesting results such as having more information is not necessarily better.

Keywords: Technology investment, competition, real options, game theory, dynamic games, incomplete information, technological systems, and technology innovation

1. Introduction Investment opportunities in new

technologies (so called real assets) can be considered as collections of real options. It is well understood that options on real assets share similarities with call options on financial securities (Dixit and Pindyck 1994). Analogous to financial options on stocks and bonds, real options are options on real or physical assets such as technologies, equipment, production facilities, oil deposits, and office buildings.

The term “invest” means a firm exercises its option by invoking an initial cost to exchange for a real asset that may pay a stream of future cash flows. This allows financial option pricing theory to be extended to value real options. Significant applications are found in capital investments, technology management, new product development, R&D, natural resources, and real estate investment (Brennan and Schwartz 1985, McDonald and Siegel 1986, Paddock, Siegel, and Smith 1988, Williams 1993, Baldwin and Clark 1994,

Strategic Exercise of Real Options: Investment Decisions in Technological Systems

258 JOURNAL OF SYSTEMS SCIENCE AND SYSTEMS ENGINEERING / Vol. 12, No. 3, September, 2003

Grenadier and Weiss 1997, and Merton 1997). On the other hand, the analogy between

financial options and real options is close but not exact. The two differ in terms of tradability, liquidity, ownership, and how the exercise of options may impact the underlying asset (Zhu 1999b). In particular, competitive interaction becomes fundamentally important in the valuation and exercise of real options, while it may not be such a significant concern for financial options. Such competitive interactions may have profound effects on option exercise decisions and the resulting equilibrium, effects that have yet to be addressed in the real options literature (Tallon, Kauffman, Lucas, Whinston, and Zhu 2002).

Unlike call options on financial securities, real options may be distinguished by whether the owner’s right to exercise the option is exclusive. Depending on how exclusive this right is, real options can be classified as proprietary or shared. Proprietary options provide exclusive rights to exercise, which may result from patents on a technology or the firm’s unique intellectual capital that competitors cannot duplicate. In contrast, shared real options are non-proprietary, “collective” opportunities of the industry, like the opportunity to introduce a new product that may be subject to close substitutes, or the chance to build a new plant to serve a particular geographic market without barriers to competitive entry.

In the real world, the luxury of proprietary options is seldom available. When the options are non-proprietary, one firm and its competitors hold an option on the same asset, and whoever exercises first may get the underlying asset. The timing of the exercise

decision could have a profound impact on the realized value of the option, which is further complicated by the joint presence of uncertainty, competition, and private information.

With oligopolistic ownership of the investment opportunity, the action of any one owner can affect the values of other assets in the portfolio, as well as the actions of other owners. Under the threat of competition, the exercise of options strategically depends on the tradeoff between the benefits and costs of going ahead with an investment against waiting for more information. Waiting can have an informational benefit (McDonald and Siegel 1986). However, if a firm chooses to defer exercising its option until better information is received (thus resolving uncertainty), it runs the risk that another firm may preempt it by exercising first (Zhu 1999a). Such an early exercise by a competitor can erode the profits or even force the option to expire prematurely.

Despite its importance, competition has been typically ignored in most of the real options literature. Only a few recent papers have started to address this issue (see, e.g., Trigeorgis 1996, Grenadier 1996, Smit and Trigeorgis 1998, and Joaquin and Butler 2000). This burgeoning body of literature has provided important insight into how competition impacts the valuation and exercise of non-proprietary options on real assets. 1 However, a key assumption in this work is that 1 In addition to real options, the literature of financial securities also has several papers that analyze the strategic exercise of warrants and convertible securities in a full information context (e.g., Emanuel 1983, Constantinides 1984, and Spatt and Sterbenz 1988).

ZHU and WEYANT

JOURNAL OF SYSTEMS SCIENCE AND SYSTEMS ENGINEERING / Vol.12, No. 3, September, 2003 259

agents have symmetric and complete information. Agents are assumed to be perfectly informed about the parameters of the option. No private and incomplete information is involved.

Asymmetric Information

Real world observation has offered us many realistic situations in which agents are imperfectly and differentially informed. Examples abound in both the financial and real options domains, though the vast majority of applications are likely to occur in the real options market. For example, Bill Gates knows better about the prospect and volatility of Microsoft’s stock options than an average market participant. Amazon.com may have better information on the cost (thus profitability) of selling books on-line than the traditional book retailers like Barnes & Nobel. Intel might have better information about the cost to produce 64-bit microprocessors than its competitors like AMD. In oil exploration, firms obtain private information about the probability of finding an oil deposit in a specific area through seismic surveys and in-house geophysics expertise. More examples exist in high tech and R&D that show how competition and asymmetric information manifests itself in technology markets. The information asymmetry among firms may be due to factors such as prior investment on R&D, learning curve in a new market, in-house expertise, and active information gathering activities like market research.

As firms often have asymmetric private information in technology or real asset investments, relaxing the full-information

assumption will add substantial realism to the state of knowledge. A few recent studies include asymmetric information in their option valuation models. Back (1993) provides an extension of the Kyle (1985) model of continuous insider trading that includes asymmetric information on financial options. While there is no strategic exercise feature in the model, information is conveyed by trading in the options. Smit and Trigeorgis (1998) examine R&D strategies using a real options’ model that contains incomplete information and signaling strategies. More recently, a doctoral dissertation at Stanford University (Zhu 1999b) develops real options and game-theoretic models for investment decisions in information technologies, in which information asymmetry and endogenous competition are explicitly modeled. Grenadier (1999) develops a continuous-time model for equilibrium option exercise with private signals, in which informational cascades and herding behavior in option exercise are analyzed.2

Despite this recent signs of advancement in the field, several problems still exist with the current literature. The most important limitations are: (1) The ordering/timing of exercise is assumed to be fixed rather than endogenously determined; (2) Payoffs are assumed to be independent of the order of exercise; (3) Informational externalities and payoff externalities are assumed to be separate rather than combined.3 Not every study in the 2 Informational herding occurs when agents ignore their own private information and instead emulate the behavior of other agents. 3 Externality occurs when one agent’s action affects another agent.



literature has all of these problems, but most of them have one or more of them. Addressing these problems systematically would likely bring the real options theory closer to reality.

Implications of Asymmetric Information to Option Pricing by Arbitrage or Equilibrium

As mentioned earlier, real assets (especially new technologies) are often subject to substantial transaction costs, indivisibility, and the inability to be sold short. We assume that the underlying technology is indivisible so that the owner cannot sell (or exercise) a small part of it in order to reveal its value. This makes the arbitrage pricing questionable. In addition, asymmetric information can itself lead to the failure to price options by arbitrage. As demonstrated by Detemple and Seldon (1991) and Back (1993), trading in the option affects the flow of information, making a seemingly redundant asset not capable of being priced by arbitrage.4 Even when an option would appear to be redundant, adding it to the market can have real consequences because its price may reveal information about the fundamental value of the asset. When the option is traded, the volatility of the underlying asset becomes stochastic as a result of the change in the information flow. This eliminates the potential for dynamically replicating the option.

Therefore, an equilibrium pricing approach

4 The option can be priced by arbitrage if it is redundant—that is, it can be created synthetically by trading the underlying asset and other assets. If the option is not redundant, then its exercise may have an effect on the underlying asset price (as well as its volatility), because prices will adjust to a new equilibrium when a nonredundant asset is created.

(instead of non-arbitrage pricing) must be used. The equilibrium approach relaxes the tradability assumptions needed for arbitrage pricing. To avoid further complication, we assume risk neutrality, so that prices are determined by discounted expected values, where the expectation is conditional on the available information. Under this risk-neutrality assumption, all assets are priced so as to yield an expected rate of return equal to the risk-free rate. This seemingly restrictive assumption can easily be relaxed by adjusting the drift rate to account for a risk premium in the manner of Cox, Ingersoll and Ross (1985).

In modeling endogenous competition and asymmetric information, this paper builds upon another line of literature, namely dynamic games (Kreps & Wilson 1982, Kreps, Milgrom, Roberts, Wilson 1982, and Cho & Kreps 1987), and asymmetric information (Hendricks & Kovenock 1989, Banerjee 1992, and Chamley & Gale 1994). The following distinctions exist between our model and those existing models in the literature: (1) Our model recognizes the option value of waiting to better resolve uncertainty--this option value is not only conceptualized but also quantified in our model; (2) We endogenize the timing and the leader-follower sequence of investment while the literature typically assumes an exogenous order of who moves first.

The rest of the paper is organized as follows. Section 2 endogenizes competition in a complete but possibly imperfect information setting. Section 3 models asymmetric information in a multi-period game tree structure. Section 4 concludes the paper.

ZHU and WEYANT


2. Competition in Option Exercise The value of a real option can be fully

captured only if it is exercised in an optimal way, which is partly contingent on correct anticipation of competitors' moves. Competitors do not exercise their options randomly. Rather they do this based on certain rational calculations. It is thus necessary to endogenize competitors’ decisions. In order to do so, we assume (1) competitors make rational calculations in determining when to exercise their options, thus exhibiting optimizing behavior; (2) each player makes decisions by monitoring an ongoing uncertain state variable and anticipating competitor’s moves; and (3) the payoffs depend on the resulting equilibrium. In this section, we assume that the firms have complete but possibly imperfect information.5 We will then move on to deal with incomplete information in the next section.

Suppose two rival firms face an investment opportunity for a new technology. Both firms can decide to invest now or wait. The investment opportunity can be deferred, implying a deferral option embedded in the investment project, as shown in Figure 1. The payoff of the investment project depends on

5 As defined in the game theory literature, perfect information means that at each move in the game the player with the move knows the full history of the play of the game thus far. That is, every information set in the game is a singleton. Imperfect information, in contrast, means that there is at least one nonsingleton information set. Complete information means that the payoff functions are common knowledge, i.e., there is no private information on payoffs, costs, or feasible strategies.

the timing of the exercise decisions of both firms. Specifically, we define the game as follows:

Players: Firm A and Firm B. Strategies: In each period, each firm

decides either to invest (I) or defer (D) in an indivisible technology that requires a lumpy investment outlay, tiI , .6 If a firm decides to invest, it also needs to decide how much to produce, i.e., a quantity ),0[ ∞∈iq (i=A, B) that maximizes its expected payoff. Hence, each firm has a strategy space );,( IqDIS ii = , (i=A, B).

Payoffs: The payoff to firm i, i.e., its expected profit ),( jii qqπ , is a function of the strategies chosen by it and its competitor. If both firms A and B invest without observing each other’s decision, they will split the market according to a Nash-Cournot equilibrium. If one firm invests first and the other does later, their payoffs will be determined through a Stackelberg leader-follower equilibrium (Fudenberg and Tirole 1991). If one firm invests first, but the other never does, then it will enjoy a monopoly position.

VAt,s(II) - It, V

Bt,s (II) - It

VAt,s (ID) - It, C

Bt,s (ID)

CAt,s(DI), VB

t,s(DI) - It

CAt,s(DD), CB

t,s (DD)

A

I

D

BI

D

I

DB

Figure 1 Simultaneous move and Nash equilibrium

In figure 1, if both firms defer and keep the option alive, the payoff would be the value of 6 tiI , may be time- and state-dependent. We also

use a simplified notation iI to denote investment outlay that is only firm specific.



the option (C) that they can decide whether or not to exercise later. The values of V and C are firm-specific and path-dependent, as indicated by the superscripts and subscripts.

2.1 Quantity Decisions and Equilibrium

Outcomes We first derive the equilibrium quantities

and payoffs from an optimization process. These will serve as building blocks in our subsequent analysis of a Nash equilibrium under endogenous competition in a multi-period game structure.

Suppose P(Θt, Q) is the inverse demand function, i.e.,

)(),( BAtt qqbQP +−Θ=Θ (1)

where tΘ is the stochastic demand-shift parameter, representing the uncertainty in market demand. tΘ is assumed to follow a log-normal diffusion process in continuous time, or a binomial process in discrete time.7 Parameter b measures the elasticity of demand, which is inversely related to the quality of the product. BA qqQ += is the aggregate quantity on the market, where Aq and Bq are the quantities produced by firms A and B, respectively. Denote Ci as firm i’s cost function, i.e.,

iiFii qcCqC +=)( , (2) where FC is the fixed cost, and ic is the marginal cost. For simplicity, assume 0=FC .

7 Since we assume managerial flexibility in output decisions, Q will be zero if demand becomes too low, thus avoiding “negative price,” a problem potentially associated with this type of demand functions.

2.1.1 Firms Move with Perfect Information If firms A and B invest sequentially, one

firm will be able to observe the other’s move. Suppose firm A invests first and firm B, upon observing A’s move, follows up. We use the backward induction method to solve the game (Fudenberg and Tirole 1991). 8

Based on backward induction, the follower’s decision is

( ) ( )( )max , max ,B B

B A B t A B B Bq qq q P q q c qπ = Θ + −

The leader’s decision is

( )( )

( )( )( )

max ,

max ,A

A

A A B Aq

t A B A A Aq

q q q

P q q q c q

π =

Θ + −

Solving the optimization problem yields the equilibrium profits:

2

2

1 ( 2 )8

1 ( 3 2 )16

i t i j

j t j i

c cb

c cb

π

π

= Θ − + = Θ − +

(3)

where the subscript i represents the leader, j the follower.

2.1.2 Firms Move with Imperfect Information

If firms A and B make their decisions without observing each other, each would have imperfect information about the other’s actual moves. This is equivalent to the situation that they invest simultaneously. Then each firm determines its optimal quantity by solving the

8 Backward induction is a solution concept for dynamic games. It works in a simple manner: go to the end of the game and work backward, one move at a time. In the leader-follower competition, backward induction analyzes the follower’s decision first, assuming the leader has already been in the market.

ZHU and WEYANT


following optimization problem:

max ( , )

max[ ( , ( )) ( )]i

i

i i jq

t i j i i iq

q q

P q q q C q

π =

Θ + −

where πi (i=A, B) is firm i’s profit, qi, qj are quantities of firms i and j respectively. Solving this optimization problem yields the equilibrium quantity:

* 1 ( 2 )3i t i jq c cb

= Θ − + , i j≠ . (4)

Then the equilibrium profit for each firm is 21 ( 2 )

9i t i jc cb

π = Θ − + (5)

It is straightforward to verify the second- order condition,

0),(

2

2

<∂

∂

i

jii

q

qqπ,

thus the quantity choices maximize the profit. Notice it is the information structure, rather

than the timing, that makes the games different. The players need not act simultaneously: it suffices that each choose a strategy without knowledge of the other’s choice, as would be the case in the Prisoner’s Dilemma if the prisoners reached decisions at arbitrary times while in separate cells. A sequential-move, unobserved-action game has the same Nash equilibrium as the simultaneous-move Cournot game.

If operating cash flows last n years, [1, )n∈ ∞ , the net present value, NPVi, of the

profit values will be:

in

t ti

iii Ik

IVNPV −∑+

=−==1 )1(

π (6)

where k is the discount rate. For perpetual operating cash flows, the NPV can be simplified as

ii

iii Ik

IVNPV −=−=π . (7)

2.2 The Multi-Period Model We use a multi-period game tree structure

as an extensive-form representation of the option-exercise game. As shown in Figure 2, two firms A and B decide either to invest (I) or defer (D) in each period. Then Nature (N) decides that the market demand will be either moving up to uΘ or down to dΘ according to a binomial process, where 1u ≥ and 1d ≤ are the multiplicative binomial parameters. Upon observing the moves made in the previous period and the development of the market demand, each firm decides again to invest or defer in the next period. The game can go on for as many periods as needed.

We analyze the multi-period game based on backward induction. Suppose the game has only one period left, at the end nodes of the game tree, the payoffs for both firms are determined by the equilibrium outcomes of the competitive investment subgames in (3) and (5), depending on what equilibrium the game ends up--Nash-Cournot, Stackelberg, or monopoly. We then use the backward induction process to figure out the subgame perfect equilibrium and then use the dynamic programming method to roll back the values from the last period to the second last one, and so on (Luenberger 1998). Once having these values in place, both firms then figure out their optimal strategies.

Equilibrium is found by solving the whole



game. Again the game is solved by backward induction, but this time the first step in working backwards from the end of the game involves solving a real game (the

simultaneous-move game between firms A and B in the final period, given the moves in the previous period) rather than solving a single-agent optimization problem.

N M M A

I D

I D

…...

I D

u d

kb - IccSL jit +−Θ= 8/)2( 2

kb - IccSF ijt +−Θ= 16/)23( 2

RCppC tt /))1(( −+ −+

RCppC tt /))1(( −+ −+

…...

2 kb-Icct +−Θ 9/)2( 21kb-Icct +−Θ 9/)2( 212

t=1

�t=i ...

厖? ..

S M S M

u d

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厖? ..

A

S M S M

u d

I D

B

I D

B

I D

B B

A

A

I D

B

I D

B

N M M A

I DA

I D

B

I D

B

t=n

Firms A and B decide either to invest (I) or defer (D) in each period. Then Nature (N) decides that the market demand will be either moving up to uΘ or down to dΘ according to a binomial process. Upon observing the moves made in the previous period and the development of the market demand, each firm decides I or D again in the next period. At the end nodes of the game tree, the payoffs for both firms are determined by the equilibrium values derived through the optimization process. Subgame perfect equilibrium is found by backward induction and dynamic programming approach.

Figure 2 Generic structure of the multi-period model

2.3 Competition Erodes Option Value Once we have the structure of the

multi-period model in place, we are ready to examine how competition affects option exercise in an imperfectly competitive market. As a benchmark, let us start with a symmetric duopoly model with imperfect information. Firms A and B are ex ante equal players − they have equal marginal cost, and none enjoys an informational advantage over the other.

Figure 3 shows such an example involving two competitors with equal marginal cost,

BA cc = . Using the approach described in the

previous section, we find that the equilibrium is (I, I),9 meaning both firms invest and obtain a profit of (25, 25). Notice they could get a profit of (198, 198) if both wait and observe the market movement, then decide to invest if the market moves up, or defer if the market moves down. Absent cooperation, however, each firm rushes to exercise its option prematurely.

9 We use a strategy pair, (firm A’s action, firm B’s action), to represent the combination of firms’ strategies. For example, (I, D) means that firm A invests and firm B defers.

ZHU and WEYANT


S447 6

M1329 0

S-219-327

M-4 0

S 6447

M 01329

S-327-219

M 0-4

N349349

M1329 0

M 01329

A00

N-243-243

M-4 0

M 0-4

A00

AI D

2525

252 3

B

I DB

I D

3252

198198

AAI D I D

u du d

AI DI D

u d

B

I D

B

I D

CA= 8CB= 8

A

B

I D

B

I DB

I D

B

I D

Using the approach described in §2.2 and the generic structure in Figure 2, the equilibrium is found to be (I, I) as

represented by the bold line, meaning both firms invest and obtain a profit of (25, 25). Parameter values are:

8== BA cc , 320 =Θ , u=1.30, d=0.77, b=1, r=10%, 3750 =I , tt rII )1(0 += .

Figure 3 Symmetric duopoly

I

D

I D

Firm A

Firm B

25, 25 252, 3

3, 252 198, 198

*

Figure 4 Suboptimal equilibrium As shown in Figure 4, this suboptimal

“rush equilibrium” falls in the classic Prisoner’s Dilemma. 10 Firms tend to move

10 We assume in this model that firms engage in non-cooperative competition. Of course, the inferior “rush equilibrium” may be improved by cooperation. If in a repeated game, cooperation is possible, because when firms interact over time threats and promises concerning future behavior may influence

early in an effort to preempt competitors or in fear of being preempted by competitors. Such fear of competitive preemption can lead to a simultaneous rush to early exercise, a

current behavior. Kreps, Milgrom, Roberts, and Wilson (1982) provide a landmark account of the role of reputation in achieving rational cooperation in a finitely repeated Prisoners’ Dilemma.



phenomenon we have often observed in real-world technology markets.

The real options literature has investigated the option value of waiting to a firm when payoffs are stochastic and investment irreversible (see, e.g., McDonald and Siegel 1986, Majd and Pindyck 1987, Dixit and Pindyck 1994). It has been shown in these studies that firms will typically delay investing until well after the point at which expected discounted benefits equal initial costs. In so doing, they exploit the option value of waiting.

The option value of waiting, however, may be overestimated when the risk of competitive erosion or preemption is omitted. As we have shown above, if other firms invest first and in so doing enjoy an advantage, the fear of competitive preemption may reduce or destroy the option value of waiting. When such strategic behavior is introduced into the standard model of option exercise, firms would exercise their options much more aggressively, a pattern that may be characterized as “racing with the competition.”

This may help explain some real world observations that companies exercise their options at a very early stage despite their ability to defer their decisions. Competition may change the investment behaviors of a firm – it may become more aggressive in making investment decisions. We have witnessed waves of acquisition and other aggressive investment behaviors where industry rivalry is intense and barriers of entry are low (as typical in the high-tech industry). One such example is the aggressive investment in Internet-based

technologies (as coined as the "dot-com" bandwagon) during 1995-2000. Many firms, especially those in Silicon Valley in the United States, concerned about falling behind on the technology curve, engaged in huge e-commerce spending without deriving any tangible benefits (Barua and Mukhopadhyay 2000). Another example is that semiconductor manufacturers sometimes continue to build capacity in the face of declining demand and increasing idle rate of capacity. This results in excess capacity for the semiconductor industry as a whole. While this kind of behavior is often regarded as irrational from a non-strategic perspective, our model provides a rational foundation for such excessive capacity building patterns in the semiconductor industry. It is the competition that leads to the “rush equilibrium” which in turn drives the aggressive capacity investment decisions.

3. Asymmetric Information After examining the effects of imperfect

competition on option exercise, we are ready to turn to information structures. As discussed in the Introduction section, information asymmetry does exist among competing firms in technology markets. Incorporating asymmetric, incomplete information will add greater realism to the model. Recall that in an option-exercise game with complete information the firms’ payoff functions are common knowledge. In a game with incomplete information, in contrast, at least one firm is uncertain about another firm’s payoff or cost functions.

ZHU and WEYANT


3.1 Model of Information Structure Information is incomplete and asymmetric.

Firm A knows its own cost function,

AAAA qcqC =)( ,

but has only incomplete information about firm B’s cost function. The following probability distribution represents firm A’s belief about firm B’s cost function:

−=

)1()(

θθ

yprobabilitwithqcyprobabilitwithqc

qCBL

BHBB

(8)

where HAL ccc << . Firm B knows both firms’ cost function, thus has superior information (Firm B could have just invented a new technology). All of this is common knowledge: firm A knows that firm B has superior information, firm B knows that firm A knows this, and so on. The demand function is the same as defined in (1).

In such a game with incomplete information, we say that firm B has two possible types, Lc and Hc , or its type space is { }HLB ccT ,= . Firm A’s type space is simply { }AA cT = . Firm B knows its own type as well as firm A’s type, while firm A is uncertain about B’s type. Formally,

( )

( ) 1A B H A A

A B L A A

P t c t c

P t c t c

θ

θ

= = =

= = = − (9)

represent firm A’s belief about firm B’s types, given its own type. It is a distinctive feature of the Bayesian equilibrium that beliefs are elevated to the level of importance of strategies

in such incomplete-information games.11

3.2 Subgame Equilibrium under Asymmetric Information

3.2.1 Simultaneous Exercises Firms A and B decide either to invest or

defer without observing each other’s moves. Since firm B knows its own cost function, it will choose an optimal quantity based on its true cost. Naturally, firm B may want to choose a lower quantity if its marginal cost is high than if it is low. Firm A, for its part, should anticipate that firm B may tailor its quantity to its cost in this way. Let )(*

HB cq and )(*LB cq

denote firm B’s quantity choices as a function of its cost, and let *

Aq denote firm A’s single quantity choice.

If firm B’s cost is Hc , it will choose )(*

HB cq to solve

max ( , ; )

max[ ( , ( )) ]B

B

B A B Hq

t A B H Bq

q q c

P q q c q

π =

Θ + −

Similarly, if B’s cost is Lc , it will choose * ( )B Lq c to solve

max ( , ; )

max[ ( , ( )) ]B

B

B A B Lq

t A B L Bq

q q c

P q q c q

π =

Θ + −

Firm A, however, has only a probability distribution on firm B’s cost function. It would have to optimize its profit under this incomplete information. Based on firm A’s current information set, firm A knows that firm B’s cost is high with probability θ and low

11 However, note that firms choose their strategies, but they do not choose their beliefs. Their beliefs are determined by the information available to them.



with probability (1-θ). It thus should anticipate that firm B’s quantity choice will be * ( )B Hq c with probability θ and * ( )B Lq c with probability (1-θ), respectively. Mathematically, firm A’s decision is to choose *

Aq to maximize its expected profit such that:

max ( , )

max{ [ ( ,( ( ))) ]

(1 )[ ( ,( ( ))) ] }

A

A

A A Bq

t A B H A Aq

t A B L A A

q q

P q q c c q

P q q c c q

π

θ

θ

=

Θ + −

+ − Θ + −

Solving the first-order conditions of these optimization problems yields the optimal quantities:

* 13

* 113 6

* 13 6

[ 2 (1 ) ]

( ) ( 2 ) ( )

( ) ( 2 ) ( )

A t A H Lb

B H t H A H Lb b

B L t L A H Lb b

q c c c

q c c c c c

q c c c c c

θ

θ

θ θ−

= Θ − + + −

= Θ − + + − = Θ − + − −

(10)

The corresponding equilibrium profits are:

* 219

* 2119 2

* 219 2

[ 2 (1 ) ]

( ) [( 2 ) ( )]

( ) [( 2 ) ( )]

A t A H Lb

B H t H A H Lb

B L t L A H Lb

c c c

c c c c c

c c c c c

θ

θ

π θ θ

π

π

−

= Θ − + + −

= Θ − + + − = Θ − + − −

(11)

The results above in (10) constitute a Bayesian Nash equilibrium, because they meet the mutual-best-response criterion. That is, each firm’s quantity choice is a best response to the other firm’s choices, given its belief about its competitor’s types.

Compare the equilibrium quantities *Aq ,

)(*HB cq , and )(*

LB cq in (10) to the Nash-Cournot equilibrium under complete information with costs Ac and Bc in (3). Assuming that the values of marginal costs are such that both firms’ equilibrium quantities are

positive, 12 firm i produces * 13i bq = ( tΘ

2 )i jc c− + in the full information case. Under incomplete information, in contrast, )(*

HB cq is greater than 1

3 ( 2 )t H Ab c cΘ − + and )(*

LB cq is less than 13 ( 2 )t L Ab c cΘ − + . This

occurs because firm B not only tailors its quantity to its own cost but also responds to the fact that firm A cannot do so. If firm B’s cost is low, for example, it produces more because its cost is low but also produces less because it knows that firm A will produce a quantity that maximizes its expected profit and thus is larger than firm A would produce if it knew firm B’s cost to be low. 3.2.2 Sequential Exercises

The ordering of sequential moves is crucial for an option-exercise game under asymmetric information, because decisions of exercise (and nonexercise) may reveal private information. Firms can infer information by moving later than others. The order of moves reflects each firm’s calculated tradeoff between the extra reward from exercising early and the informational benefit from waiting to learn competitors’ private information through their revealed actions.

In the literature, the ordering of actions has been typically assumed to be pre-determined. In contrast, we allow the ordering of exercise to be endogenously determined through agents’ optimizing decisions. Two sequences are possible: 12 Suppose Hc is not so high that the high cost firm produces nothing. The sufficient condition to rule out this problem is 1

3 ( 2 )H t Ac c< Θ + .

ZHU and WEYANT


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

According to backward induction, we first solve the follower’s decision, i.e.,

( )( )

( )( )((

( ))) ] ( )

( )( )

( )( )((

( ))) ] ( )

max , , max ,

max , , max ,

B H B H

B L B L

B A B H t A Bq c q c

B H H B H

B A B L t A Bq c q c

B L L B L

q q c P q q

q c c q c

q q c P q q

q c c q c

π

π

= Θ

+ −

= Θ + −

then the leader’s decision,

( ) ( )( )( ){] ( ) ( ( )( )) ] }

*

*

max , max ,

1 ,

A AA A B t A B Hq q

A A t A B L A A

q q P q q c

c q P q q c c q

π θ

θ

= Θ +

− + − Θ + −

The solutions to the above optimization problems are

* 12

* 114 4

* 14 4

[ 2 (1 ) ]

( ) ( 3 2 ) ( )

( ) ( 3 2 ) ( )

A t A H Lb

B H t H A H Lb b

B L t L A H Lb b

q c c c

q c c c c c

q c c c c c

θ

θ

θ θ−

= Θ − + + −

= Θ − + + − = Θ − + − −

(12)

Then the corresponding equilibrium profits are

* 218

* 2116

* 2116

[ 2 (1 ) ]

( ) [( 3 2 ) (1 )( )]

( ) [( 3 2 ) ( )]

A t A H Lb

B H t H A H Lb

B L t L A H Lb

c c c

c c c c c

c c c c c

π θ θ

π θ

π θ

= Θ − + + −

= Θ − + + − − = Θ − + − −

(13)

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

If the firm with private information moves first, the follower would have an opportunity to infer its private information through revealed actions. More specifically, firm A would

observe B’s quantity choices, )(*HB cq or

)(*LB cq , and infer firm B’s cost function, Hc

or Lc , accordingly. Thus, the private information of the more-informed firm may become public via its exercise decisions. As a consequence of this information revelation, information asymmetry may be mitigated.

Upon learning firm B’s private information, firm A chooses its quantity to maximize its profit. Conditional on that firm A learned

HB cc = , firm A’s decision would be: *

*

max ( , ( ))

max[ ( , ( ( ))) ]A

A

A A B Hq

t A B H A Aq

q q c

P q q c c q

π =

Θ + −.

Similarly, conditional on that firm A learned LB cc = , firm A’s decision would be:

*

*

max ( , ( ))

max[ ( , ( ( ))) ]A

A

A A B Lq

t A B L A Aq

q q c

P q q c c q

π =

Θ + −.

Anticipating firm A’s above response, firm B solves for )( HB cq when its true cost is

Hc , i.e., *

( )

*

( )

max ( , ( ))

max [ ( , ( ( ) ( ))) ] ( )B H

B H

B A B Hq c

t A B B H H B Hq c

q q c

P q q q c c q c

π =

Θ + −

By the same reasoning, firm B solves for

( )LB cq when its true cost is Lc , i.e.,

*

( )

*

( )

max ( , ( ))

max [ ( , ( ( ) ( ))) ] ( )B L

B L

B A B Lq c

t A B B L L B Lq c

q q c

P q q q c c q c

π =

Θ + −

Solving these optimization problems yields the following equilibrium quantities:

Conditional on HB cc = ,



* 14

* 12

( ) ( 3 2 )

( ) ( 2 )A H t A Hb

B H t H Ab

q c c c

q c c c

= Θ − +

= Θ − + (14)

Conditional on LB cc = , * 1

4* 1

2

( ) ( 3 2 )

( ) ( 2 )A L t A Lb

B L t L Ab

q c c c

q c c c

= Θ − +

= Θ − + (15)

The corresponding equilibrium profits are: * 21

16* 21

8

( ) ( 3 2 )

( ) ( 2 )A H t A Hb

B H t H Ab

c c c

c c c

π

π

= Θ − +

= Θ − + (16)

* 2116

* 218

( ) ( 3 2 )

( ) ( 2 )A L t A Lb

B L t L Ab

c c c

c c c

π

π

= Θ − +

= Θ − + (17)

where (16) is conditional on HB cc = , while (17) is conditional on LB cc = .

3.3 The Multi-period Model under

Asymmetric Information

We use a multi-period game tree structure, like in Section 2.2, as an extensive-form representation of the option-exercise game. At the end nodes of the game tree, the payoffs for both firms are determined by the equilibrium values derived in the previous section. Depending on what equilibrium the game ends up, the values are in (11), (13), (16) or (17). We then use the backward induction process to find out the Bayesian subgame perfect equilibrium and then use the dynamic programming approach to roll back the values from period t to period (t-1). Once having the values of these various possibilities, each firm decides its best strategy. Notice that the game essentially regenerates itself if it reaches a (D, D) branch. In other word, the game beginning in the (D, D) path (should it be reached) is just

like the game as a whole (beginning in the first period). The only difference is that tΘ may have evolved into a new level, and the firms may have missed the cash flows in the previous periods while they were waiting. This feature helps simplify the equilibrium analysis for a multi-period game. To see how asymmetric information manifests itself in option-exercise games, consider the following two scenarios. 3.3.1 When Firm A Has Fairly Accurate

Belief about Firm B’s Cost An option-exercise game with asymmetric

information is illustrated in Figure 5. Firm A’s belief about firm B’s cost is

( ) 0.2A B HP c c θ= = = , or equivalently, ( ) 1 0.8A B LP c c θ= = − = . This means firm A

believes that there is 80% chance firm B’s type is low cost, while firm B itself knows its true cost is Lc . Thus firm A’s information is fairly accurate. Using backward induction, the equilibrium is found to be (D, I), meaning that the more informed player (B) invests while the less informed player (A) waits. Under the parameter values given above, the profits are found to be (0, 603) for firms A and B respectively. 3.3.2 When Firm A Has Less Accurate but

More “Optimistic” Belief about B’s Cost

Another scenario is shown in Figure 6, where firm A has less accurate but more “optimistic” assessment on B’s true cost, i.e.,

( ) 0.8A B HP c c θ= = = . Using the same approach as above, the equilibrium is found to have changed to (I, I), meaning that both firms A and B invest, resulting in a profit of (66, 109) for firms A and B respectively.

ZHU and WEYANT


θ = 0.2CA= 8CH= 10CL= 6*

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Using backward induction, the equilibrium is found to be (D, I). The equilibrium profits are found to be (0, 603) for firms A and B respectively under the following parameter assumptions: 2.0=θ , 8=Ac , 10=Hc ,

6=Lc , 320 =Θ , u=1.30, d=0.77, b=1, r=10%, 3750 =I , tt rII )1(0 += .

Figure 5 Asymmetric duopoly scenario 1: When firm A has fairly accurate belief about B’s cost

A00

θ = 0.8CA= 8CH= 10CL= 6*

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u d

The only difference between Figures 5 and 6 is that θ changed from 0.2 to 0.8. This means that firm A has less accurate but more “optimistic” assessment on B’s true cost. The equilibrium is found to have changed to (I, I), resulting in a profit of (66, 109) for firms A and B respectively. Parameter values are: 8.0=θ , 8=Ac ,

10=Hc , 6=Lc , 320 =Θ , u=1.30, d=0.77, b=1, r=10%, 3750 =I , tt rII )1(0 += .

Figure 6 Asymmetric duopoly scenario 2: When firm A has less accurate but more “optimistic” belief about B’s cost



3.4 Having Better Information May Hurt

You! As shown in these two scenarios, if θ is low

(e.g., θ =0.2), meaning firm A has fairly accurate belief about firm B’s cost. The game ends up in the equilibrium (D, I), because this belief leads firm A to behave conservatively as it believes its competitor is a strong one (with low cost). On the other hand, if θ is high enough (e.g., θ=0.8), firm A “confidently” believes that firm B is a weak player (with high cost). This “optimistic” (though inaccurate) belief leads firm A to behave aggressively, resulting in the (I, I) Nash equilibrium.

Surprisingly, the more accurate assessment on competitor’s cost function actually leads to lower equilibrium profits for firm A, as shown in Table 1.

Table 1 Beliefs and equilibrium profits π (A) π (B)

θ = 0.2 0 603

θ = 0.8 66 109

This happens because the belief leads the firm to behave more conservatively and its competitor knows this and thus behaves more aggressively. For this reason, having better information may actually hurt a firm!

The observation that firm A does worse when it has better information illustrates an important difference between single- and multi-agent decision problems. In single-agent decision theory, having more information can never make the decision maker worse off. In game theory, however, having more

information (or more precisely, having it known to the other players that one has more information) can make a player worse off.

3.5 Option Exercise Generates Both

Information and Payoff Externalities As discussed in the Introduction section, a

key assumption typically used in the literature is that each agent’s payoff is independent of the ordering of exercise. Everyone who chooses the right decision gets the same reward regardless of how many others chose this decision before or after her (see, e.g., Banerjee 1992). While this assumption greatly simplifies the model, it could lead to some unrealistic equilibria (such as the most informed agent may end up the worst off.). There exist many situations in which the ordering does matter and may matter a great deal.

Our model relaxes this assumption. Doing so allows us to endogenize both the payoff structure and the ordering of exercise. Our model shows that the option exercise of one firm impacts not only the information set of the other firm but also the actual payoffs from exercising the option. There is extra reward for being the first to exercise the option (so called “first-mover advantage”), while at the same time private information of the first mover is revealed, enabling the followers to “free ride” on the leaders’ private information. We have thus combined two types of externalities in our model: the informational externality and the payoff externality.

The existence of asymmetric information leads naturally to attempts by the informed to communicate or mislead and to attempts by the

ZHU and WEYANT


uninformed to learn or respond. Thus information asymmetry may induce gaming behaviors. 13 For example, a high-cost firm would try to masquerade as a low-cost player. However, such signals would have to be credible if they were to change competitors’ beliefs or behaviors. One such credible strategy might be to make a strategic investment in a new technology by incurring an irreversible cost. Doing so may induce the competitor into believing that the firm has invented a low-cost technology and cause it to behave more conservatively. Many other types of information signaling exist, but they are out of the scope of this paper.

3.6 Extensions The above model and analysis can be

extended to more periods than the above examples. We just roll the equilibrium payoffs of period t back to the previous period (t-1) until we reach the beginning period of the game. Based on the NPVi’s of various possibilities, each firm decides its best strategies. Figure 7 illustrates how the model works in a multi-period setting. The investment opportunity remains available for 3 periods, instead of 2 as shown in Figures 5 and 6 (in the case of more periods, same procedure applies repeatedly). Since the option is still alive at the end of period 2, its unexercised value is not zero. Instead, this value would

13 We assume that only actions are credible in communicating private information. Cheap talks like press release cannot be informative: all firms with superior information prefer to be perceived as low cost, regardless their true costs. So there cannot exist an equilibrium in which cheap talks affect competitors’ actions.

have to be determined through the option-exercise equilibrium in the remaining periods. Notice the path in bold lines (D, I)→(u, D), firm B has already invested in period 1, but firm A remains uncommitted at the end of the second period because the demand (thus the profit as a Stackelberg follower) is still not high enough to justify the investment. Firm A waits for another period, and then decides to invest when the demand is further up, but to let the option expire if the demand is down. If firm A invests, two firms would share the market in a Stackelberg leader-follower equilibrium. If firm A lets the option expires without exercise, then firm B would enjoy monopoly profit. The payoff from the subgame-perfect equilibrium can be calculated by the formula we derived earlier. The same procedure applies to all other branches of the game tree. We then solve the whole game backward and find out the equilibrium is (D, I), meaning that firm B (the better-inform firm) exercise the option first while firm A waits. Consistent with the case in Figure 5, the option-exercise equilibrium is again sequential, with the better-informed firm moving first.

Notice the present values of the equilibrium payoff are (0, 603) in Figure 5 and (82, 578) in Figure 7. Thus, longer option life gives higher payoff to the less-informed firm, while the payoff for the better-informed firm could be higher if its competitor does not enter or lower if the competitor does. The reason is that the longer option life gives the informationally disadvantaged firm more opportunities to infer the leader’s private information.



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The figure illustrates how the model works in a multi-period setting. The parameters are the same as in Figure 5 except that the game is one more period longer. Using backward induction, the equilibrium is found to be (D, I). Consistent with the case in Figure 5, the option-exercise equilibrium is again sequential, with the better-informed firm moving first. The equilibrium profits are (82, 578) for firms A and B respectively. Thus longer option life gives higher payoff to firm A.

Figure 7 Asymmetric information: More periods If there are more than two firms in the

option-exercise game, for any individual firm what matters is whether one of the (n-1) other firms invests earlier than it. To represent multiple players, we can use a multi-player game tree. 14 A key difference may arise as players are added, however. As the number of firms increases, the likelihood of informational herding or investment cascade may increase substantially.15

14 The purpose of our model is mainly to analyze duopoly or oligopoly situations, where the number of competing firms is limited. If there are too many players, the difference that each of them could make may become negligible. That would be a different situation from what we try to model. 15 See Banerjee (1992) and Grenadier (1999) for further discussions on informational herding and investment cascade.

4. Conclusions Most of the real options literature has

focused on market environments without strategic interactions. On the other hand, the industrial organization literature endogenizes market structure, yet it typically ignores uncertainty and the option value of waiting. Considering the joint effects of uncertainty and competition, this paper integrates the game-theoretic models of strategic market interactions with a real options approach to investment under uncertainty.

Unlike the literature, we suppose that firms have incomplete information about each other’s cost (i.e., type). This leads to Bayesian

ZHU and WEYANT


Nash equilibria that we have analyzed in detail. The main focus of our research, in contrast to others in the literature, is to model asymmetric information and its impact on option-exercise strategies and the resulting Bayesian Nash equilibrium.

We have attempted to capture this through developing a multi-period, game-theoretic model. The dynamic equilibrium nature of this model differs significantly from that of the current literature on real options. In the standard models of option exercise, the ordering of agents’ moves is typically assumed to be exogenous and not determined by any sort of optimizing behavior. In our model, however, both timing and ordering are the essence of the game; agents exercise strategically and the sequence of exercise is endogenous. We have shown that the option exercise strategies under asymmetric information can be very different from those under full information. Our results also show how competition erodes option value, and why having better information may actually hurt a firm.

In addition, our results complement and extend the literature by showing that the ordering of sequential option exercise reveals private information. The firm that invests first captures more profits, while the firm that invests later gets an opportunity to learn the private information of the leader. Thus option exercise generates both informational and payoff externalities in the sense that the exercise decision of one firm may affect both the payoff and the information set of its competitors. The results obtained here serve to

add greater realism to the theory of technology investment under asymmetric information.

The economic insights gained through the model may have certain implications in real investment decisions. For example, firms considering investing in a new technology need to strategically consider how their investment payoffs may be affected by their competitors’ moves. They also need to balance the first-mover advantage against the informational benefits of moving later, as private information may be revealed from the sequential exercise of such real options in technology markets.

5. Acknowledgements We are grateful to William Sharpe, Blake

Johnson, Steve Grenadier, Robert Wilson, Jim Sweeney, David Luenberger, and the seminar participants at Stanford University for constructive discussions on our research. The usual disclaimer applies.

References [1] Back, K., “Asymmetric information and

options”, Review of Financial Studies, Vol.6, pp435-472, 1993.

[2] Baldwin, C. and K. Clark, “Modularity- in-design: An analysis based on the theory of real options”, working paper, Harvard Business School, Cambridge, MA, 1994

[3] Banerjee, A.V., “A simple model of herd behavior”, Quarterly Journal of Economics, Vol.107, No.3, pp797-817, 1992

[4] Barua, A., and T. Mukhopadhyay, “Information technology and business performance: Past, present and future,” in Framing the Domains of IT Management:



Projecting the Future through the Past, R.W. Zmud (ed.), Pinnaflex Education Resources, Inc., 2000.

[5] Brennan, M. and E. Schwartz, “Evaluating natural resource investments”, Journal of Business, Vol.58, No.2, pp135-57, 1985.

[6] Chamley, C. and D. Gale, “Information revelation and strategic delay in a model of investment”, Econometrica, Vol.62, No.5, pp1065-85, 1994.

[7] Cho, I.-K., and D. Kreps, Signaling games and stable equilibria, Quarterly Journal of Economics Vol.102, No.2, pp179-221, 1987.

[8] Constantinides, G.M., “Warrant exercise and bond conversion in competitive market”, Journal of Financial Economics, Vol.13, pp371-397, 1984.

[9] Cox, J.C., J.E. Ingersoll, and S.A. Ross, “An inter temporal general equilibrium model of asset prices”, Econometrica, Vol.53, pp363-384, 1985.

[10] Detemple, J., and L. Selden, “A general equilibrium analysis of option and stock market interactions”, International Economic Review, Vol.32, pp279-303, 1991.

[11] Dixit, A.K. and R. S. Pindyck, Investment under Uncertainty, Princeton University Press, Princeton, NJ, 1994.

[12] Emanuel, D.C., “Warrant valuation and exercise strategy”, Journal of Financial Economics, Vol.12, pp211-235, 1983.

[13] Fudenberg, D. and Tirole, J., Game Theory, MIT Press, Cambridge, MA, 1991.

[14] Grenadier, S.R., “The strategic exercise of options: development cascades and overbuilding in real estate markets”, Journal

of Finance, Vol.51, No.5, pp1653-1679, 1996.

[15] Grenadier, S.R. and A. Weiss, “Investment in technological innovations: An option pricing approach”, Journal of Financial Economics, Vol.44, pp397-416, 1997.

[16] Grenadier, S.R., “Information revelation through option exercise”, Review of Financial Studies, Vol.12, No.1, pp95-129, 1999.

[17] Hendricks, K. and D. Kovenock, “Asymmetric information, information externalities, and efficiency: the case of oil exploration”, Rand Journal of Economics, Vol.20, No.2, pp164-182, 1989.

[18] Joaquin, D.C. and K.C. Butler, Competitive investment decisions: a synthesis, in New Developments in the Theory and Applications of Real Options, by M.J. Brennan and L. Trigeorgis (eds.), Oxford University Press, 2000.

[19] Kreps, D., P. Milgrom, J. Roberts, and R. Wilson, “Rational cooperation in the finitely repeated Prisoner’s Dilemma”, Journal of Economic Theory, Vol.27, pp245-52, 1982.

[20] Kreps, D. and R. Wilson, “Sequential equilibrium”, Econometrica, Vol.50, No.4, pp863-94, 1982.

[21] Kyle, A.S., “Continuous auctions and insider trading”, Econometrica, Vol.53, pp1315-1335, 1985.

[22] Luenberger, D. G., Investment Science, Oxford University Press, New York, NY, 1998.

[23] Majd, S. and R. Pindyck, “Time to build, option value, and investment decisions”, Journal of Financial Economics, Vol.18, No.1, pp7-27, 1987.

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[24] McDonald, R. and D. Siegel, “The value of waiting to invest”, Quarterly Journal of Economics, Vol.104, No.1, pp707-27, 1986.

[25] Merton, Robert, C., Nobel Lecture, Applications of Option-Pricing Theory: Twenty-Five Years Later, December 9, The Nobel Foundation, 1997.

[26] Paddock, J.L., D.R. Siegel, and J.L. Smith, “Option valuation of claims on real assets: the case of offshore petroleum leases”, The Quarterly Journal of Economics, Vol.103, pp479-508, 1988.

[27] Smit, H.T.J. and L. Trigeorgis, “R&D Option Strategies”, working paper, Erasmus University and University of Chicago, 1998.

[28] Spatt, C.S. and F.T. Sterbenz, “Warrant exercise, dividends, and reinvestment policy”, Journal of Finance, Vol.43, pp493-506, 1988.

[29] Tallon, P., R. Kauffman, H. Lucas, A. Whinston, and K. Zhu, “Using real options analysis for evaluating uncertain investments in information technology,” Communications of the Association for Information Systems (CAIS), Vol.8, pp. 136-167, 2002. Available at http://web.gsm. uci.edu/kzhu/PDFfiles/CAIS_journalarticle.pdf.

[30] Trigeorgis, L., Real Options, The MIT Press, Cambridge, MA, 1996.

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Kevin Zhu received his Ph.D. degree from Stanford University and is currently on the faculty of the Graduate School of Management, University of California, Irvine, USA. 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 involves both economic modeling and empirical investigation. His work has been accepted for publication in journals such as Information Systems Research, European Journal of Information Systems, Electronic Markets, and Communications of the ACM. One of his papers has won the Best Paper Award of the International Conference on Information 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 (voted by MBA and executive MBA students). 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 B.S./M.S. in Aeronautical Engineering and Astronautics, M.S. degrees in Engineering Management and in Operations Research and Statistics all from Rensselaer Polytechnic Institute, and a Ph.D. in Management Science with minors in Economics, Operations Research, and Organization Theory from

University of California at Berkeley. 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.

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