Title: The Truth Behind the Myth of the Folk Theorem
Abstract:We study the problem of computing an $\epsilon$-Nash equilibrium in repeated games. Earlier work by Borgs et al. [2010] suggests that this problem is intractable. We show that if we make a slight chan...We study the problem of computing an $\epsilon$-Nash equilibrium in repeated games. Earlier work by Borgs et al. [2010] suggests that this problem is intractable. We show that if we make a slight change to their model---modeling the players as polynomial-time Turing machines that maintain state ---and make some standard cryptographic hardness assumptions (the existence of public-key encryption), the problem can actually be solved in polynomial time. Our algorithm works not only for games with a finite number of players, but also for constant-degree graphical games.
As Nash equilibrium is a weak solution concept for extensive form games, we additionally define and study an appropriate notion of a subgame-perfect equilibrium for computationally bounded players, and show how to efficiently find such an equilibrium in repeated games (again, making standard cryptographic hardness assumptions).Read More
Publication Year: 2013
Publication Date: 2013-12-04
Language: en
Type: preprint
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Cited By Count: 2
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