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
kzhu@uci.edu
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.
ISSN 1004-3756/03/1203/257
CN11- 2983/N ©JSSSE 2003
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,
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Vol. 12, No. 3, pp257-278, September, 2003
Strategic Exercise of Real Options: Investment Decisions in Technological Systems
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
258
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).
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ZHU and WEYANT
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.
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Strategic Exercise of Real Options: Investment Decisions in Technological Systems
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.
(instead of non-arbitrage pricing) must be used.
Implications of Asymmetric Information to
Option Pricing by Arbitrage or Equilibrium
assume risk neutrality, so that prices are
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
The
equilibrium
approach
relaxes
the
tradability assumptions needed for arbitrage
pricing. To avoid further complication, we
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
to be redundant, adding it to the market can
between our model and those existing models
have real consequences because its price may
in the literature: (1) Our model recognizes the
reveal information about the fundamental
option value of waiting to better resolve
value of the asset. When the option is traded,
uncertainty--this option value is not only
the volatility of the underlying asset becomes
conceptualized but also quantified in our
stochastic as a result of the change in the
model; (2) We endogenize the timing and the
information flow. This eliminates the potential
leader-follower sequence of investment while
for dynamically replicating the option.
the literature typically assumes an exogenous
Therefore, an equilibrium pricing approach
order of who moves first.
The rest of the paper is organized as
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.
260
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.
JOURNAL OF SYSTEMS SCIENCE AND SYSTEMS ENGINEERING / Vol. 12, No. 3, September, 2003
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
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, I i ,t .6 If a firm decides to
invest, it also needs to decide how much to
produce, i.e., a quantity qi ∈ [0, ∞) (i=A, B)
that maximizes its expected payoff. Hence,
each firm has a strategy space S i = ( I , D; qi I ) ,
(i=A, B).
Payoffs: The payoff to firm i, i.e., its
expected profit π i (q i , q j ) , 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, VBt,s (II) - It
I
B
I
D
VAt,s (ID) - It, CBt,s (ID)
D
I
CAt,s(DI), VBt,s(DI) - It
A
B
D
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.
CAt,s(DD), CBt,s (DD)
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
I i ,t may be time- and state-dependent. We also
use a simplified notation I i to denote investment
outlay that is only firm specific.
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Strategic Exercise of Real Options: Investment Decisions in Technological Systems
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
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 π B ( q A , qB ) = max  P ( Θt , ( q A + qB ) ) − cB  qB
qB
subsequent analysis of a Nash equilibrium
under
endogenous
competition
in
The leader’s decision is
a
max π A ( q A , qB ( q A ) ) =
multi-period game structure.
qA
function, i.e.,
P (Θ t , Q ) = Θ t − b ( q A + q B )
(1)
(
)
max  P Θt , ( q A + qB ( q A ) ) − c A  q A

qA 
Suppose P(Θt, Q) is the inverse demand
where Θ t
qB
Solving the optimization problem yields the
equilibrium profits:
is the stochastic demand-shift
π = 1 (Θ − 2c + c ) 2
i
j
 i 8b t

π j = 1 (Θ t − 3c j + 2ci ) 2
16b

parameter, representing the uncertainty in
market demand. Θ t is assumed to follow a
(3)
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.
Q = q A + qB
is
the
aggregate
quantity on the market, where q A and q B are
the quantities produced by firms A and B,
respectively. Denote Ci as firm i’s cost function,
i.e.,
C i (q i ) = C F + ci q i ,
(2)
where C F is the fixed cost, and ci is the
marginal cost. For simplicity, assume C F = 0 .
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.
262
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.
JOURNAL OF SYSTEMS SCIENCE AND SYSTEMS ENGINEERING / Vol. 12, No. 3, September, 2003
ZHU and WEYANT
following optimization problem:
where k is the discount rate. For perpetual
operating cash flows, the NPV can be
simplified as
max π i (qi , q j ) =
qi
max[ P (Θt , (qi + q j )) qi − Ci (qi )]
qi
NPVi = Vi − I i =
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:
qi* = 1 (Θt − 2ci + c j ) , i ≠ j .
3b
(4)
Then the equilibrium profit for each firm is
π i = 1 (Θt − 2ci + c j ) 2
(5)
9b
It is straightforward to verify the secondorder condition,
∂π i2 (qi , q j )
∂qi2
< 0,
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,
n ∈ [1, ∞) , the net present value, NPVi, of the
profit values will be:
n
NPVi = Vi − I i = ∑
πi
t =1 (1 +
k )t
− Ii
(6)
πi
k
− Ii .
(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 u ≥ 1 and d ≤ 1 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
JOURNAL OF SYSTEMS SCIENCE AND SYSTEMS ENGINEERING / Vol.12, No. 3, September, 2003
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Strategic Exercise of Real Options: Investment Decisions in Technological Systems
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
A
I
t=1
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.
D
B
B
D
I
I
…
...
…
...
(Θt − 2c1+ c2) 2/ 9kb-I
(Θt − 2c2 + c1) 2/ 9kb-I
I
B
I
t=n
S
A
d
D
I
I
A
M
A
I
D
S
I
M
SF = ( Θ t − 3c j + 2 c i ) 2 / 16 kb - I
S
M
M
S
N
B
I
M
M
A
I
D
D
厖
? ..
d
B
D
SL = ( Θ t − 2 c i + c j ) 2 / 8 kb - I
−
−
u
B
D
+
+
( pC t + (1 − p )C t ) / R
( pC t + (1 − p )C t ) / R
u
d
u
t=i
...
D
D
B
D
I
A
N
B
D
I
M
M
D
A
厖
? ..
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
previous section, we find that the equilibrium
2.3 Competition Erodes Option Value
is (I, I),9 meaning both firms invest and obtain
Once we have the structure of the
a profit of (25, 25). Notice they could get a
multi-period model in place, we are ready to
profit of (198, 198) if both wait and observe
examine how competition affects option
the market movement, then decide to invest if
exercise in an imperfectly competitive market.
the market moves up, or defer if the market
As a benchmark, let us start with a symmetric
moves down. Absent cooperation, however,
duopoly model with imperfect information.
each firm rushes to exercise its option
Firms A and B are ex ante equal players − they
prematurely.
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,
c A = c B . Using the approach described in the
264
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.
JOURNAL OF SYSTEMS SCIENCE AND SYSTEMS ENGINEERING / Vol. 12, No. 3, September, 2003
ZHU and WEYANT
I
A
D
CA= 8
CB= 8
B
B
D
I
I
252
3
25
25
u
3
252
B
S
447
6
198
198
A
u
d
u
d
I
I
D
D
I
A
B
D
M
1329
0
I
S
-219
-327
A
I
D
I
M
-4
0
M
0
1329
S
6
447
S
-327
-219
M
0
-4
N
349
349
I
D
B
B
D
A
I
D
B
D
d
I
D
M
M
1329
0
0
1329
A
0
0
N
-243
-243
B
D
M
-4
0
I
M
0
-4
D
A
0
0
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:
c A = c B = 8 , Θ 0 = 32 , u=1.30, d=0.77, b=1, r=10%, I 0 = 375 , I t = I 0 (1 + r )t .
Figure 3 Symmetric duopoly
Firm B
I
I
D
*
25, 25
252, 3
3, 252
198, 198
Firm A
D
Figure 4 Suboptimal equilibrium
As shown in Figure 4, this suboptimal
early in an effort to preempt competitors or in
“rush equilibrium” falls in the classic
fear of being preempted by competitors. Such
10
Prisoner’s Dilemma. Firms tend to move
fear of competitive preemption can lead to a
simultaneous rush to early exercise, a
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
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.
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Strategic Exercise of Real Options: Investment Decisions in Technological Systems
phenomenon we have often observed in
real-world technology markets.
technologies (as coined as the "dot-com"
The real options literature has investigated
especially those in Silicon Valley in the United
the option value of waiting to a firm when
States, concerned about falling behind on the
payoffs
technology
are
stochastic
and
investment
bandwagon) during 1995-2000. Many firms,
curve,
engaged
in
huge
irreversible (see, e.g., McDonald and Siegel
e-commerce spending without deriving any
1986, Majd and Pindyck 1987, Dixit and
tangible benefits (Barua and Mukhopadhyay
Pindyck 1994). It has been shown in these
2000). Another example is that semiconductor
studies that firms will typically delay investing
manufacturers sometimes continue to build
until well after the point at which expected
capacity in the face of declining demand and
discounted benefits equal initial costs. In so
increasing idle rate of capacity. This results in
doing, they exploit the option value of waiting.
excess capacity for the semiconductor industry
The option value of waiting, however, may
as a whole. While this kind of behavior is often
be overestimated when the risk of competitive
regarded as irrational from a non-strategic
erosion or preemption is omitted. As we have
perspective, our model provides a rational
shown above, if other firms invest first and in
foundation
so doing enjoy an advantage, the fear of
building patterns in the semiconductor industry.
competitive preemption may reduce or destroy
It is the competition that leads to the “rush
the option value of waiting. When such
equilibrium”
strategic behavior is introduced into the
aggressive capacity investment decisions.
standard model of option exercise, firms would
exercise their options much more aggressively,
This may help explain some real world
such
which
excessive
in
turn
capacity
drives
the
3. Asymmetric Information
a pattern that may be characterized as “racing
with the competition.”
for
After examining the effects of imperfect
competition on option exercise, we are ready to
turn to information structures. As discussed in
observations that companies exercise their
the
options at a very early stage despite their
asymmetry does exist among competing firms
ability to defer their decisions. Competition
in
may change the investment behaviors of a firm
asymmetric, incomplete information will add
– it may become more aggressive in making
greater realism to the model. Recall that in an
investment decisions. We have witnessed
option-exercise
waves of acquisition and other aggressive
information the firms’ payoff functions are
investment behaviors where industry rivalry is
common
intense and barriers of entry are low (as typical
incomplete information, in contrast, at least
in the high-tech industry). One such example is
one firm is uncertain about another firm’s
the aggressive investment in Internet-based
payoff or cost functions.
266
Introduction
technology
section,
markets.
game
knowledge.
information
Incorporating
with
In
a
complete
game
with
JOURNAL OF SYSTEMS SCIENCE AND SYSTEMS ENGINEERING / Vol. 12, No. 3, September, 2003
ZHU and WEYANT
in such incomplete-information games.11
3.1 Model of Information Structure
Information is incomplete and asymmetric.
Firm A knows its own cost function,
C A (q A ) = c A q A ,
3.2.1 Simultaneous Exercises
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:
c q
C B (q B ) =  H B
c L q B
with probability θ
with probability (1 − θ )
(8)
where c L < c A < c H . Firm B knows both
firms’ cost
function,
thus
3.2 Subgame Equilibrium under
Asymmetric Information
has
superior
information (Firm B could have just invented a
new technology). All of this is common
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 q *B (c H ) and q *B (c L )
denote firm B’s quantity choices as a function
of its cost, and let q *A denote firm A’s single
quantity choice.
If firm B’s cost is c H , it will choose
*
q B (c H ) to solve
max π B (q A , qB ; cH ) =
knowledge: firm A knows that firm B has
qB
superior information, firm B knows that firm A
max[ P (Θt , (q A + qB )) − cH ] qB
knows this, and so on. The demand function is
qB
the same as defined in (1).
In
such
a
game
with
incomplete
information, we say that firm B has two
Similarly, if B’s cost is c L , it will choose
q*B (cL ) to solve
max π B (q A , qB ; cL ) =
possible types, c L and c H , or its type space
qB
is TB = {c L , c H } . Firm A’s type space is
max[ P (Θt , (q A + qB )) − cL ] qB
simply T A = {c A } . Firm B knows its own type
as well as firm A’s type, while firm A is
uncertain about B’s type. Formally,
 PA (tB = cH t A = c A ) = θ

 PA (tB = cL t A = c A ) = 1 − 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
qB
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.
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Strategic Exercise of Real Options: Investment Decisions in Technological Systems
with probability (1-θ). It thus should anticipate
that firm B’s quantity choice will be q*B (cH )
with probability θ and q*B (cL ) with
probability (1-θ), respectively. Mathematically,
*
firm A’s decision is to choose q A to
maximize its expected profit such that:
max π A (qA , qB ) =
positive,
12
firm i produces
qi* =
1
3b
(Θt
− 2ci + c j ) in the full information case. Under
incomplete information, in contrast, q *B (c H )
is
greater
q *B (c L )
than
is less than
(Θt − 2cH + c A ) and
(Θt − 2cL + c A ) . This
1
3b
1
3b
occurs because firm B not only tailors its
quantity to its own cost but also responds to
qA
max{θ [ P(Θt ,(qA + qB (cH ))) − cA ] qA
the fact that firm A cannot do so. If firm B’s
+(1 − θ )[ P(Θt ,(qA + qB (cL ))) − cA ] qA }
cost is low, for example, it produces more
qA
Solving the first-order conditions of these
optimization problems yields the optimal
quantities:
q*A = 31b [Θt − 2c A + θ cH + (1 − θ )cL ]
 *
(10)
1−θ
1
qB (cH ) = 3b (Θt − 2cH + cA ) + 6b (cH −cL )
 *
θ
1
 q B ( c L ) = 3 b ( Θ t − 2c L + c A ) − 6 b ( c H − c L )
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
The corresponding equilibrium profits are:
information, because decisions of exercise (and
π *A = 91b [Θt − 2cA + θ cH + (1 − θ )cL ]2
 *
2
1−θ
1
π B (cH ) = 9b [(Θt − 2cH + c A ) + 2 (cH −cL )]
 *
2
θ
1
π B (cL ) = 9b [(Θt − 2cL + cA ) − 2 (cH −cL )]
nonexercise) may reveal private information.
(11)
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
The results above in (10) constitute a
informational benefit from waiting to learn
Bayesian Nash equilibrium, because they meet
competitors’ private information through their
the mutual-best-response criterion. That is,
revealed actions.
each firm’s quantity choice is a best response
In the literature, the ordering of actions has
to the other firm’s choices, given its belief
been typically assumed to be pre-determined.
about its competitor’s types.
In contrast, we allow the ordering of exercise
Compare the equilibrium quantities q *A ,
q *B (c H ) , and
q *B (c L )
in (10) to the
Nash-Cournot equilibrium under complete
information with costs c A and c B in (3).
to be endogenously determined through agents’
optimizing decisions. Two sequences are
possible:
12
Assuming that the values of marginal costs are
Suppose cH is not so high that the high cost firm
produces nothing. The sufficient condition to rule
such that both firms’ equilibrium quantities are
out this problem is cH < 13 (Θt + 2c A ) .
268
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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 π ( q , q , c ) = max  P Θ , ( q ( q )
t
A
B
 qB ( c H ) B A B H
qB ( c H ) 

+ q B ( cH ) ) − cH ] q B ( cH )


 max π B ( q A , qB , cL ) = max  P Θt , ( q A ( qB )
q B ( cL )
 qB ( c L )

+ q B ( cL ) ) − cL ] q B ( cL )

)
(
)
then the leader’s decision,
{ (
max π A ( q A , qB ) = max θ  P Θt ,

qA
qA
(
(
q A + q*B
( cH ) ) )
observe B’s quantity choices, q *B (c H ) or
q *B (c L ) , and infer firm B’s cost function, c H
or
c L , 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
c B = c H , firm A’s decision would be:
max π A (q A , q*B (cH )) =
qA
max[ P (Θt , (q A + q*B (cH ))) − c A ] q A
))
−c A ] q A + (1 − θ )  P ( Θt , q A + q*B ( cL ) − c A ] q A }
The solutions to the above optimization
problems are
q*A = 21b [Θt − 2c A + θ cH + (1 − θ )cL ]
 *
1−θ
1
qB (cH ) = 4b (Θt − 3cH + 2c A ) + 4b (cH −cL )
 *
θ
1
qB (cL ) = 4b (Θt − 3cL + 2c A ) − 4b (cH −cL )
(12)
Then the corresponding equilibrium profits
are
π *A = 81b [Θt − 2c A + θ cH + (1 − θ )cL ]2
 *
2
1
π B (cH ) = 16b [(Θt − 3cH + 2c A ) + (1 − θ )(cH −cL )]
 *
2
1
π B (cL ) = 16b [(Θt − 3cL + 2c A ) − θ (cH −cL )]
(13)
Sequence 2: The more-informed firm (B)
moves first and the less-informed firm (A)
follows
.
qA
Similarly, conditional on that firm A
learned c B = c L , firm A’s decision would be:
max π A (q A , q*B (cL )) =
qA
max[ P (Θt , (q A + q*B (cL ))) − c A ] q A
.
qA
Anticipating firm A’s above response, firm
B solves for q B (c H ) when its true cost is
c H , i.e.,
max π B (q*A , qB (cH )) =
q B ( cH )
max [ P (Θt , (q*A (qB ) + qB (cH ))) − cH ] qB (cH )
q B ( cH )
By the same reasoning, firm B solves for
q B (cL ) when its true cost is c L , i.e.,
max π B (q*A , qB (cL )) =
q B ( cL )
max [ P(Θt , (q*A (qB ) + qB (cL ))) − cL ] qB (cL )
q B ( cL )
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
Solving these optimization problems yields
the following equilibrium quantities:
Conditional on c B = c H ,
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269
Strategic Exercise of Real Options: Investment Decisions in Technological Systems
q*A (cH ) =
 *
qB (cH ) =
1
4b
(Θt − 3c A + 2cH )
1
2b
( Θ t − 2c H + c A )
(14)
Conditional on c B = c L ,
*
q A (cL ) =
 *
qB (cL ) =
1
4b
(Θt − 3c A + 2cL )
1
2b
( Θ t − 2c L + c A )
(15)
The corresponding equilibrium profits are:
π *A (cH ) = 161b (Θt − 3c A + 2cH ) 2
(16)
 *
2
1
π
(
c
)
(
2
c
c
)
=
Θ
−
+
 B H
t
H
A
8b
π *A (cL ) = 161b (Θt − 3c A + 2cL ) 2
(17)
 *
2
π B (cL ) = 81b (Θt − 2cL + c A )
where (16) is conditional on c B = c H , while
(17) is conditional on c B = c L .
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
270
like the game as a whole (beginning in the first
period). The only difference is that Θt 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
PA (cB = cH ) = θ = 0.2 , or equivalently,
PA (cB = cL ) = 1 − θ = 0.8 . 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 c L . 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.,
PA (cB = cH ) = θ = 0.8 . 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.
JOURNAL OF SYSTEMS SCIENCE AND SYSTEMS ENGINEERING / Vol. 12, No. 3, September, 2003
ZHU and WEYANT
I
A
D
B
θ = 0.2
CA= 8
CH= 10
CL= 6*
B
D
I
I
217
87
-14
154
0
603
d
u
B
A
u
d
D
A
I
I
M
1329
0
I
M
-4
0
M
0
1125
S
-93
670
M
0
-101
S
-373
-103
N
294
526
d
I
M
1329
0
D
B
B
D
A
I
D
B
D
S
-249
-249
A
I
D
B
D
S
385
153
167
298
u
I
I
D
M
0
1125
A
0
0
B
D
I
D
N
-270
-151
D
I
M
0
-101
M
-4
0
A
0
0
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: θ = 0.2 , c A = 8 , c H = 10 ,
c L = 6 , Θ 0 = 32 , u=1.30, d=0.77, b=1, r=10%, I 0 = 375 , I t = I 0 (1 + r )t .
Figure 5 Asymmetric duopoly scenario 1: When firm A has fairly accurate belief about B’s cost
I
I
B
A
D
B
D
I
288
47
66
109
u
d
B
S
511
83
D
0
603
A
230
263
u
d
u
I
I
D
I
A
I
D
B
D
M
1329
0
θ = 0.8
CA = 8
CH= 10
CL= 6*
I
S
-187
-288
A
M
-4
0
I
S
-93
670
M
0
1125
S
-373
-103
The only difference between Figures 5 and 6 is that
M
0
-101
θ
N
406
465
M
1329
0
I
M
0
1125
D
B
B
D
A
I
D
B
D
d
I
D
A
0
0
B
D
N
-215
-184
M
-4
0
I
M
0
-101
D
A
0
0
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: θ = 0.8 , c A = 8 ,
c H = 10 , c L = 6 , Θ 0 = 32 , u=1.30, d=0.77, b=1, r=10%, I 0 = 375 , I t = I 0 (1 + r ) t .
Figure 6 Asymmetric duopoly scenario 2:
When firm A has less accurate but more “optimistic” belief about B’s cost
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Strategic Exercise of Real Options: Investment Decisions in Technological Systems
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
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
accurate belief about firm B’s cost. The game
Information and Payoff Externalities
ends up in the equilibrium (D, I), because this
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
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
272
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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.
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
3.6 Extensions
The above model and analysis can be
the
subgame-perfect
equilibrium
can
be
extended to more periods than the above
calculated by the formula we derived earlier.
examples. We just roll the equilibrium payoffs
The same procedure applies to all other
of period t back to the previous period (t-1)
branches of the game tree. We then solve the
until we reach the beginning period of the
whole game backward and find out the
game. Based on the NPVi’s of various
equilibrium is (D, I), meaning that firm B (the
possibilities, each firm decides its best
better-inform firm) exercise the option first
strategies. Figure 7 illustrates how the model
while firm A waits. Consistent with the case in
works
The
Figure 5, the option-exercise equilibrium is
investment opportunity remains available for 3
again sequential, with the better-informed firm
periods, instead of 2 as shown in Figures 5 and
moving first.
in
a
multi-period
setting.
6 (in the case of more periods, same procedure
Notice the present values of the equilibrium
applies repeatedly). Since the option is still
payoff are (0, 603) in Figure 5 and (82, 578) in
alive at the end of period 2, its unexercised
Figure 7. Thus, longer option life gives higher
value is not zero. Instead, this value would
payoff to the less-informed firm, while the
payoff for the better-informed firm could be
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.
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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Strategic Exercise of Real Options: Investment Decisions in Technological Systems
A
I
D
B
B
I
I
D
547
140
-14
154
82
578
d
u
B
385
153
228
298
u
A
I
I
D
u
d
D
I
A
D
I
I
I D
825
247
-249
-249
233
0
145
974
-93
670
d
u
厖
? ..
I
257
1524
A
-373
-103
D
0
2601
I
-279
178
A
0
76
294
526
0
321
-279
178
A
B
I
D
804
296
A
I
D
B
B
D
106
974
I
507
771
-270
-151
I
D
178
0
0
76
D
0
143
d
u
D I
d
D
B
B
D
A
D
0
321
I
-416
-261
A
D
厖
? ..
厖
? ..
0
-310
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
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,
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.
274
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
JOURNAL OF SYSTEMS SCIENCE AND SYSTEMS ENGINEERING / Vol. 12, No. 3, September, 2003
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
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.
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
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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/.
JOURNAL OF SYSTEMS SCIENCE AND SYSTEMS ENGINEERING / Vol.12, No. 3, September, 2003
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Strategic Exercise of Real Options: Investment Decisions in Technological Systems
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
278
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.
JOURNAL OF SYSTEMS SCIENCE AND SYSTEMS ENGINEERING / Vol. 12, No. 3, September, 2003