2.1 Structures of interaction and theories of practical rationality
Two persons, each with but two possible actions. Four possible outcomes. The Prisoner's Dilemma is the simplest structure of interaction in which, if each person, in choosing that action which, given the other person's choice, maximizes his own expected utility, the outcome will afford each of the persons less (expected) utility than would the outcome were each to choose his other, non-maximizing action.
In many situations with this structure, it is plausible to think of a person who chooses not to maximize as cooperating, or seeking to cooperate, with the other person. They do better working together than working alone. The person who seeks to maximize his utility, given the other's choice, may then be represented, perhaps somewhat pejoratively, as defecting from the cooperative arrangement. But since Ken Binmore, who is one of the leading defenders of the rationality of maximizing choice, is happy to use the terminology of cooperate and defect, I shall follow his example.
Most economists, like Binmore, and some philosophers, believe that it is rational for persons to choose the action that they judge will maximize their expected utility. In the Prisoner's Dilemma, each person sees that, if the other cooperates, then he will maximize his expected utility by defecting. Each also sees that if the other defects, he will also maximize his expected utility by defecting. So defecting is the maximizing choice for him, whatever the other does. So Binmore claims – and it is here that I shall part company with him – it is rational for each to defect. Although each would expect greater utility if they cooperated.
In situations more complex than the Prisoner's Dilemma, there may be no choice among a person's possible actions that will maximize his expected utility whatever the other persons do. But suppose we restrict ourselves to interactions with finitely many persons each with finitely many possible actions – hardly onerous restrictions.