The myth of the Folk Theorem

Christian Borgs, Jennifer Chayes, Nicole Immorlica, Adam Tauman Kalai, Vahab Mirrokni and Christos Papadimitriou

Games and Economic Behavior, 2010, vol. 70, issue 1, 34-43

Abstract: The Folk Theorem for repeated games 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 Nash equilibrium for a three-player infinitely-repeated game is as hard as it is in two-player one-shot games. More specifically, for any two-player game, we give a simple construction of a three-player game whose Nash equilibria (even under repetition) correspond to those of the one-shot two-player game. Combined with recent computational hardness results for one-shot two-player normal-form games ([Daskalakis et al., 2006], [Chen et al., 2006] and [Chen et al., 2007]), this gives our main result: the problem of finding an (epsilon) Nash equilibrium in a given n×n×n game (even when all payoffs are in {-1,0,1}) is PPAD-hard (under randomized reductions).

Keywords: Repeated; games; Computable; general; equilibrium; models (search for similar items in EconPapers)
Date: 2010
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0899-8256(09)00078-5
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:gamebe:v:70:y:2010:i:1:p:34-43

Access Statistics for this article

Games and Economic Behavior is currently edited by E. Kalai

More articles in Games and Economic Behavior from Elsevier
Bibliographic data for series maintained by Catherine Liu ().