Abstract
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 4.10. 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 coming at a price, namely the existence of a multitude of outcomes attainable in equilibrium. Such an embarrassment of riches is expressed by a so-called folk theorem.
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Notes
- 1.
In this proposition it is assumed that G ∞(δ) is well-defined, in particular that the discounted payoff sums are finite.
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Peters, H. (2015). Repeated Games. In: Game Theory. Springer Texts in Business and Economics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46950-7_7
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