Dominick Salvatore Schaums Outline of Microeconomics, 4th edition Schaums Outline Series 2006

CHAP. 12] GAME THEORY AND OLIGOPOLISTIC BEHAVIOR 279
(b)
(c)
Auto makers face a prisoners’ dilemma in introducing yearly style changes if each auto maker introduces
yearly style changes only to avoid losing a great deal of sales, but introducing yearly style changes
reduces every auto maker’s profit.
Each member of a cartel has an incentive to cheat because by cheating it can increase its profits over and
above those that it would receive without cheating. However, when every cartel member cheats, each will
earn less profit than if no member cheated.
12.10 Explain whether or not the duopolists in a Cournot equilibrium face a prisoners’ dilemma.
The duopolists in a Cournot equilibrium do face a prisoners’ dilemma because each adopts its dominant strategy but
could do better by coordination (i.e., by choosing to jointly produce the monopoly output and share equally in the
higher profits).
12.11 Explain how the 1971 law that banned cigarette advertising on television solved the prisoners’ dilemma
for cigarette producers.
Before the 1971 law that banned cigarette advertising on television, each producer spent too much on advertising
and this cut into its profits. Yet, no producer would unilaterally reduce its advertising because others would then
have an incentive to continue advertising heavily to increase their market share and profits. While the 1971 law
that banned TV cigarette advertising was intended to discourage smoking (and to some extent the law achieved
its purpose), it also had the unintended effect of solving the prisoners’ dilemma for cigarette producers. Specifically,
by being forced to reduce TV advertising, cigarette producers were able to reduce costs and increase profits—
something that they had been unable to do on their own.
12.12 From the payoff matrix of Table 12.8, where the payoffs (the negative values) are the years of possible
imprisonment for individuals A and B, determine (a) whether individual A has a dominant strategy, (b)
whether individual B has a dominant strategy, (c) the optimal strategy for each individual. (d ) Do individuals
A and B face a prisoners’ dilemma?
Table 12.8
Individual A
Individual B
Confess Don’t Confess
Confess 25, 25 21, 210
Don’t Confess 210, 21 22, 22
(a) Individual A has the dominant strategy of confessing because if individual B confesses, individual A gets a
5-year sentence if he also confesses and a 10-year sentence if he does not. Similarly, if individual B does not
confess, individual A gets a 1-year sentence if he confesses and a 2-year sentence if he does not confess.
(b) For individual B the dominant strategy is also to confess because if individual A confesses, individual B gets a
5-year sentence if he also confesses and a 10-year sentence if he does not. Similarly, if individual A does not
confess, individual B gets a 1-year sentence if he confesses and a 2-year sentence if he does not confess.
(c) The optimal strategy for each individual is to adopt his dominant strategy, which is to confess.
(d ) Individuals A and B face the prisoners’ dilemma. That is, when each individual adopts his dominant strategy of
confessing, each gets a 5-year sentence. However, if each did not confess, each would get a 2-year sentence only.
PRICE AND NONPRICE COMPETITION AND CARTEL CHEATING
12.13 Explain why the payoff matrix in Problem 12.3 indicates that firms A and B face the prisoners’ dilemma.
We have seen in the answer to Problem 12.3(c) that each firm adopts its dominant strategy of charging the low price
and earns a profit of 1 (see the top left cell of the payoff matrix in Problem 12.3(c). Each firm, however, would earn a
profit of 2 if each charged a high price (see the bottom right cell). But that could only be achieved through
cooperation. Thus, firms A and B face the prisoners’ dilemma.