In the famous prisoners’ dilemma game the bad (Pareto inferior) outcome, resulting from each player playing his dominant action, cannot be avoided in a Nash equilibrium or subgame perfect Nash equilibrium even if the game is repeated a finite number of times, cf. Problem 4.8(a)–(c). As we will see in this chapter, this bad outcome can be avoided if the game is repeated an infinite number of times. This, however, is going to have a price, namely the existence of a multitude of outcomes attainable in equilibrium. Such an embarrassment of richness is expressed by a so-called Folk theorem.
As was illustrated in Problem 4.8(d)–(g), also finite repetitions of a game may sometimes lead to outcomes that are better than (repeated) Nash equilibria of the original game. See also [9] and [37].
In this chapter we consider two-person infinitely repeated games and formulate Folk theorems both for subgame perfect and for Nash equilibrium. The approach is somewhat informal, and mainly based on examples. In Sect. 7.1 we consider subgame perfect equilibrium and in Sect. 7.2 we consider Nash equilibrium.
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© 2008 Springer-Verlag Berlin Heidelberg
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(2008). Repeated Games. In: Game Theory. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69291-1_7
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