Global Nash Convergence of Foster and Young's Regret Testing

UPF Economics and Business Working Paper No. 788

31 Pages Posted: 29 Mar 2005

See all articles by Fabrizio Germano

Fabrizio Germano

Universitat Pompeu Fabra - Department of Economics and Business

Gabor Lugosi

Universitat Pompeu Fabra - Department of Economics and Business (DEB)

Date Written: October 2004

Abstract

We construct an uncoupled randomized strategy of repeated play such that, if every player follows such a strategy, then the joint mixed strategy profiles converge, almost surely, to a Nash equilibrium of the one-shot game. The procedure requires very little in terms of players' information about the game. In fact, players' actions are based only on their own past payoffs and, in a variant of the strategy, players need not even know that their payoffs are determined through other players' actions. The procedure works for general finite games and is based on appropriate modifications of a simple stochastic learning rule introduced by Foster and Young.

Keywords: Regret testing, regret based learning, random search, stochastic dynamics, uncoupled dynamics, global convergence to Nash equilibria

JEL Classification: C72, C73, D81, D83

Suggested Citation

Germano, Fabrizio and Lugosi, Gabor, Global Nash Convergence of Foster and Young's Regret Testing (October 2004). UPF Economics and Business Working Paper No. 788, Available at SSRN: https://ssrn.com/abstract=678622 or http://dx.doi.org/10.2139/ssrn.678622

Fabrizio Germano (Contact Author)

Universitat Pompeu Fabra - Department of Economics and Business ( email )

Ramon Trias Fargas 25-27
Barcelona, 08005
Spain
+34-93-542-2729 (Phone)
+34-93-542-1746 (Fax)

Gabor Lugosi

Universitat Pompeu Fabra - Department of Economics and Business (DEB) ( email )

Barcelona, 08005
Spain

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