Introduction and examples

In many situations of interest, the strategic context involves a given number of players who interact in a repeated fashion over time – e.g., the firms serving a common market, the provider of a certain service and her regular customers, or the members of a sports club. Often, it may also happen that the conditions underlying the interaction remain more or less constant throughout the process. (Thus, referring to the former examples, the aggregate demand and production technology faced by the firms are largely stable, the service provided remains essentially the same, or the activities of the club do not experience any significant change.) Then, we see in this chapter that the players' repeated interaction introduces rich intertemporal considerations that often have an important bearing on the outcome. More precisely, interesting behavior may arise in the repeated game that would be unattainable (say, it would not be consistent with equilibrium) in a one-shot play of the constituent stage game.

As a first illustration of matters, let us consider the prisoner's dilemma, whose payoffs are recalled in Table 8.1.

If this game is played only once, we know that (D, D) is the unique Nash equilibrium because D is a dominant strategy for each player. Now suppose this game is repeated a certain number of times, say T, between the same two players. Further assume that, at each t = 1, 2, …, T, both players are fully informed of what happened at all prior t′ < t.