# 11.4 The Oligopoly Version of the Prisoner’s Dilemma

The members of an oligopoly can face a prisoner’s dilemma, also. If each of the oligopolists cooperates in holding down output, then high monopoly profits are possible. Each oligopolist, however, must worry that while it is holding down output, other firms are taking advantage of the high price by raising output and earning higher profits.

Fig 11.2 shows the prisoner’s dilemma for a two-firm oligopoly—known as a duopoly. If Firms A and B both agree to hold down output, they are acting together as a monopoly and will each earn \$1,000 in profits. However, both firms’ dominant strategy is to increase output. The Nash Equilibrium is shown by the bottom right-hand corner payoffs, where each firms earn \$400 in profits.

 Firm B Hold Down Output (cooperate with other firm) Increase Output (do not cooperate with other firm) Firm A Hold Down Output (cooperate with other firm) A gets \$1,000, B gets \$1,000 A gets \$200, B gets \$1,500 Increase Output (do not cooperate with other firm) A gets \$1,500, B gets \$200 A gets \$400, B gets \$400

Fig 11.2

Why don’t the firms trust each other and why won’t they co-operate? Consider the situation of Firm A:

• If A thinks that B will cheat on their agreement and increase output, then A will increase output, too, because for A the profit of \$400 when both firms increase output (the bottom right-hand choice in Fig 11.2) is better than a profit of only \$200 if A keeps output low and B raises output (the upper right-hand choice in the table).
• If A thinks that B will cooperate by holding down output, then A may seize the opportunity to earn higher profits by raising output. After all, if B is going to hold down output, then A can earn \$1,500 in profits by expanding output (the bottom left-hand choice in the table) compared with only \$1,000 by holding down output as well (the upper left-hand choice in the table).

Thus, firm A will reason that it makes sense to expand output if B holds down output and that it also makes sense to expand output if B raises output. Again, B faces a parallel set of decisions that will lead B also to expand output.

The result of this prisoner’s dilemma is often that even though A and B could make the highest combined profits by cooperating in producing a lower level of output and acting like a monopolist, the two firms may well end up in a situation where each increase output and earn only \$400 each in profits.