Many social interactions are repeated either with the same person or with people who are drawn from the same social group. Indeed, since one-off encounters typically occur only between strangers, the analysis of repeated games promises to extend the scope of game theory considerably.
In addition, when the same game is played repeatedly the strategic options for players expand significantly, becoming in the process more life-like in a number of respects. For instance, it becomes possible to condition what you do on what your opponent has done in previous rounds. Thus you can punish or reward your opponent depending on what they have done in the past. By definition, this cannot be done when the game is played only once. Likewise players learn things about their opponents from the way they have behaved in the past. Such learning can be exploited by players behaving in particular ways to develop reputations for playing the game in particular ways. Therefore the analysis of repeated games also promises further insights regarding the types of behaviour which we might expect from instrumentally rational players.
This chapter considers repeated games in various settings. We begin with the finitely repeated prisoners’ dilemma game in section 6.2 and make use of backward induction and the subgame perfect Nash equilibrium concept from section 3.3. Perhaps somewhat surprisingly, mutual defection remains the only Nash equilibrium. The following two sections discuss, respectively, indefinitely repeated prisoners’ dilemma and the related free rider games. We show (section 6.4) that mutual cooperation is a possible Nash equilibrium outcome in these games provided there is a ‘sufficient’ degree of uncertainty over when the repetition will cease. There are some significant implications here both for liberal political theory and for the explanatory power of game theory. We notice that this result means that mutual cooperation might be achieved without the intervention of a collective agency like the State and/or without appealing to some expanded notion of rational agency (see Chapter 5). In other words cooperation could