for either player and the optimal strategy for either player depends on what each
player believes to be the strategy of the other players, the result is a nonstrictly
dominant strategy. Normal-form game A game in which each player is aware of
the strategy
firm can offer the product, at least initially, at a lower price to compensate the
consumer for the risk of trying the new brand, or the firm can adopt an
advertising campaign designed to convince the consumer that the new brand is
superior. Either market
Econometrica, 18 (1950a), pp. 155162. . Equilibrium Points in n-Person
Games. Proceedings of the National Academy of Sciences, USA, 36 (1950b), pp.
4849. . A Simple Three-Person Poker Game (with Lloyd S. Shapley).
Annals of Mathematics Study, 24 (1950c).
out branch should be disregarded in future moves. In the resulting extensiveform
game, diagrammed in Figure 13.19, we see that the optimal strategy for
Microcorp is (Enter, Enter). The final optimal strategy profile is cfw_Simple, (Enter,
Enter), which yi
second wager is riskier because the spread, or dispersion, of the possible payoffs
is greater. Each has the same expected value, but the swing between a gain and a
loss is considerably greater. It is this dispersion in the possible payoffs that is the
dis
of buyers and sellers. Firms in perfectly competitive industries were described as
price takers because of their inability in influence the market price through
individual production decisions. Consumers in such markets may similarly be
described as price
game? b. What is the Nash equilibrium for each subgame? c. Use backward
induction to find the subgame perfect equilibrium. 13.13 Suppose that the
multistage game for Alex, Andrew, and Adam is as shown in Figure E13.13. a.
What are the subgames for this ga
however, suppose that there are 50 offer 604 introduction to game theory
counteroffer rounds. Since neither Andrew nor Adam knows anything about the
others personal circumstances, let us further assume that any delay in reaching
an agreement reduces the g
than that. In capital budgeting terminology, the time value of $97.50 in the 49th
round for Adam is the same as the time value of $100 in the 50th round. But this
is not the end of the game. Adam also knows that delays in reaching an
agreement will reduce
value of a set of random outcomes. The mean is the sum of the products of each
outcome and the probability of its occurrence. When the probability of the
occurrence of each outcome is the same as the probability of every other
outcome, the mean is the sum
accepting and rejecting the offer. Denote player As discount rate as dA and Player
Bs discount rate as dB. A bargaining game has a unique subgame perfect
equilibrium if in the first round player B offers player A (13.15) as a share of the
surplus, where q
each room and asks the player to reveal his or her hand. After inspecting the hand
of each player, the referee declares a winner. Both versions of this game may be
called simultaneous-move games. Do you agree? If not, then why not? 13.2 A
subgame perfect
planning to buy another car anyway, the theft has the introduced a higher than
usual level of anxiety into the situation. Failure to quickly come to terms on the
purchase price of a replacement car may result not only in high psychological
opportunity cos
exercise 13.4. form game shown in Figure E13.6. What is the Nash equilibrium for
this game? 13.7 Suppose that the simultaneous move game in Exercise 13.6 was
modeled as a sequential-move game, with Magna moving first. a. Illustrate the
extensive form of t
Figure 13.23. We will assume for simplicity that negotiations involve only two
offers and that Andrew makes the first offer, which is denoted as P1. This is
indicated as the first branch of the decision tree.After Andrew has made the
offer,Adam can either
the two wagers, s1 2 and s2 2 are Since s2 2 > s1 2 , then the second wager is
riskier than the first. An alternative way to express the riskiness of a set of random
outcomes is the standard deviation. The standard deviation is simply the square
root of t
that is less than $100. Moreover, accepting the offer ignores the fact that Adam
has the ability to make a more advantageous (to him) counteroffer in the next
round of negotiations. What all this means is that no matter what Andrews initial
offer was, he
matrix reflects managements desire for labor to work hard and labors desire to
take it easy. Management has two options. Managers can either secretly monitor
614 introduction to game theory Firm B Dont cheat Cheat Firm A Dont cheat (10,
10) ( 5, 20) Cheat
without impatience. extended bargaining process. Similarly, if Adam has the first
move and there are an even number of rounds of negotiations, it will in both
parties interest for Andrew to accept Adams initial offer $100. In this case, Adam
will extract
the difference between a strictly dominant strategy and a weakly dominated
strategy. 13.10 It is not possible to have multiple Nash equilibria in the presence
of a subgame perfect equilibrium. Do you agree with this statement? If not, why
not? 13.11 In a
axis. The three total utility of money functions in Figure 14.1 illustrate the
concepts of constant marginal utility of money (CMUM), increasing marginal
utility of money (IMUM), and diminishing marginal utility of money (DMUM).
When conditions of increas
discount rates and 50 negotiating rounds Adam received $26.33 and Andrew
received $23.67. b. qA = 1 - dA = 0.90; qB = 1 - dB = 0.95. Substituting these values
into expression (13.15) we obtain The amount of the surplus that Adam should
offer Andrew is The
players possible strategies and payoffs from alternative strategies in a
simultaneous-move game. Simultaneous-move games may be either
noncooperative or cooperative. In contrast to noncooperative games, players of
cooperative games engage in collusive beh
game theory 14 621 We have assumed throughout most of this book that the
economic decisions were made under conditions of complete certainty. It was
assumed that the decisions of both consumers and producers were based on
complete and accurate knowledge o
process is continued, eventually Andrew and Adam will evenly divide the surplus;
but as long as Adam moves last, he will enjoy an advantage, however slight, over
Andrew. BARGAINING WITH ASYMMETRIC IMPATIENCE Suppose that instead of
maintaining an even kee
partial ignorance, are identical, the process of evaluating outcomes under
conditions of complete ignorance requires alternative approaches to the decisionmaking 622 Risk and Uncertainty process. In spite of these distinctions, we will
refer to all situat
retailer and wholesaler, and so on, are the norm, rather than the exception. As an
exercise, the reader is asked to consider why market power and the ability to
bargain with product suppliers allow large retail outlets, such as Home Depot,
Sports Authorit
1 FIGURE 14.2 Investor riskreturn indifference curves. answer to this question is
yes, but only if the investment project with the highest expected rate of return is
acceptable. It should be readily apparent from Figure 14.3 that only riskreturn
combinati
the individual gains 222 utility units. Suppose, on the other hand, that the
individual flips tails and loses $1,000.The individuals new money wealth is now
$49,000. The individuals total utility of money is U = 100(49,000)0.5 = 22,136
units. In this case