The myth of the folk theorem

  • Authors:

  • Christian Borgs;Jennifer Chayes;Nicole Immorlica;Adam Tauman Kalai;Vahab Mirrokni;Christos Papadimitriou

  • Affiliations:

  • Microsoft Research, Redmond, WA, USA;Microsoft Research, Redmond, WA, USA;Centrum voor Wiskunde en Informatica, Amsterdam, Netherlands;Georgia Institute of Technology, Atlanta, GA, USA;Microsoft Research, Redmond, WA, USA;U.C. Berkeley, Berkeley, CA, USA

  • Venue:
  • STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
  • Year:
  • 2008

Quantified Score

Hi-index 0.00

Visualization

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.