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

CHAP. 12] GAME THEORY AND OLIGOPOLISTIC BEHAVIOR 273
Table 12.1
Firm A
Firm B
Advertise Don’t Advertise
Advertise 4, 3 5, 1
Don’t Advertise 2, 5 3, 2
12.3 NASH EQUILIBRIUM
The Nash equilibrium occurs when each player has chosen his or her optimal strategy, given the strategy
chosen by the other player.
EXAMPLE 2. The payoff matrix in Table 12.2 is same as the payoff matrix in Table 12.1, except that the first number in
the bottom right cell was changed from 3 to 6. Now firm B has a dominant strategy (as in Example 1) but firm A does not.
Thus, if firm B advertises, firm A should also advertise. If firm B does not advertise, firm A earns a profit of 5 if it advertises
and 6 if it does not. This might occur, for example, if advertising adds more to firm’s A costs than to its revenue. The highadvertising
strategy for firm A and firm B is the Nash equilibrium, because given that firm B chooses its dominant strategy of
advertising, the optimal strategy for firm A is also to advertise. Not all games have a Nash equilibrium, and some games can
have more than one Nash equilibrium (see Problem 12.7).
Table 12.2
Firm A
Firm B
Advertise Don’t Advertise
Advertise 4, 3 5, 1
Don’t Advertise 2, 5 6, 2
12.4 THE PRISONERS’ DILEMMA
Prisoners’ dilemma refers to the situation where each player adopts his or her dominant strategy but could
do better by cooperating. The name comes from the case where two individuals arrested on suspicion of having
committed a crime adopt their dominant strategy of confessing and receiving more jail time than if they
cooperated (i.e., did not confess). Oligopolistic firms often face an analogous prisoners’ dilemma problem in
deciding their best business strategy.
EXAMPLE 3. Two suspects are arrested for armed robbery and, if convicted, each could receive a maximum sentence of 10
years imprisonment. Unless one or both suspects confess, however, there is only evidence to convicted them for possessing
stolen goods, which carries a maximum sentence of 1 year in prison. Each suspect is interrogated separately and no communication
is allowed between them. The district attorney promises each suspect that by confessing, he or she will go free while the
other suspect (who does not confess) will receive the full 10-year sentence. If both suspects confess, each gets a reduced
sentence of 5 years imprisonment. The (negative) payoff matrix in terms of years of detention is given in Table 12.3.
Table 12.3
Suspect A
Suspect B
Confess Don’t Confess
Confess 5, 5 0, 10
Don’t Confess 10, 0 1, 1