Cooperative Games

These three examples have the following things in common:

In each case, there are two decision-makers.
The payoffs to each decision-maker depends on both decisions.
Both decision-makers seek their own interests.
Each chooses in isolation from the other, taking the other decision as given.
As a result, both have relatively bad outcomes -- long prison terms or zero profits.

The Prisoners' Dilemma has been influential throughout the social sciences, in the second half of the 1900's, because it offers such a vivid illustration of how this can happen: rational and self-interested decision-makers, choosing their strategies in isolation from one another, find that the strategies interact so that they both have bad outcomes.

In application to the problem of oligopoly pricing, the examples given so far seem to give strong support to the second hypothesis of oligopoly pricing, the hypothesis that oligopoly prices will be the same as those in a P-competitive market: zero profits. But that's not really so clear.

The key assumption in these examples is assumption 4 -- that each chooses in isolation from the other, taking the other decision as given. But is it really rational for them to do so? In the Prisoners' Dilemma game, the isolation is imposed by the rules of the game -- the Prisoners have been isolated by the Police, and have no choice in the matter. But the oligopolists could, in principle, get together, agree on a common strategy, and share out the gains from it among themselves. They wouldn't be taking one anothers' strategies as given. Instead, they would be coordinating their strategies.

Of course, antitrust laws are designed to make such a price-fixing agreement illegal. But we haven't always had antitrust laws -- they were enacted because many people believed that businessmen were collaborating to fix high prices. And even now, there may be ways to get around the law.

When the decision-makers in a "game" get together, agree on a common strategy, and share out the gains from it among themselves, the agreement they come to is called a "cooperative solution" to the game. The examples we have looked at so far are "noncooperative solutions."

It appears that we cannot rule out the possibility of a cooperative solution to the oligopoly pricing game, so we need to look a bit at the cooperative alternative in game theory.