Global Nash Convergence of Foster and Young's Regret Testing
UPF Economics and Business Working Paper No. 788
31 Pages Posted: 29 Mar 2005
Date Written: October 2004
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: Suggested Citation