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The myth of the folk theorem

Published: 17 May 2008 Publication History

Abstract

A well-known result in game theory known as "the Folk Theorem" suggests that finding Nash equilibria in repeated games should be easier than in one-shot games. In contrast, we show that the problem of finding any (approximate) Nash equilibrium for a three-player infinitely-repeated game is computationally intractable (even when all payoffs are in {-1,0,1}), unless all of PPAD can be solved in randomized polynomial time. This is done by showing that finding Nash equilibria of (k+1)-player infinitely-repeated games is as hard as finding Nash equilibria of k-player one-shot games, for which PPAD-hardness is known (Daskalakis, Goldberg and Papadimitriou, 2006; Chen, Deng and Teng, 2006; Chen, Teng and Valiant, 2007). This also explains why no computationally-efficient learning dynamics, such as the "no regret" algorithms, can be "rational" (in general games with three or more players) in the sense that, when one's opponents use such a strategy, it is not in general a best reply to follow suit.

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cover image ACM Conferences
STOC '08: Proceedings of the fortieth annual ACM symposium on Theory of computing
May 2008
712 pages
ISBN:9781605580470
DOI:10.1145/1374376
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 17 May 2008

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  1. folk theorem
  2. nash equilibrium
  3. ppad

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STOC '08: Symposium on Theory of Computing
May 17 - 20, 2008
British Columbia, Victoria, Canada

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  • (2018)Testing for families of distributions via the fourier transformProceedings of the 32nd International Conference on Neural Information Processing Systems10.5555/3327546.3327671(10084-10095)Online publication date: 3-Dec-2018
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  • (2011)Rational Generating Functions and Integer Programming GamesOperations Research10.1287/opre.1110.096459:6(1445-1460)Online publication date: 1-Nov-2011
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