A Foundation for Markov Equilibria in Sequential Games with Finite Social Memory

TitleA Foundation for Markov Equilibria in Sequential Games with Finite Social Memory
Publication TypeJournal Article
Year of Publication2013
AuthorsMorris S, Bhaskar V, Mailath GJ
JournalReview of Economic Studies
Volume80
Issue3
Pagination - 948
Date PublishedJuly 2013
ISBN Number0034-6527, 0034-6527
KeywordsGames, Noncooperative Games (C72), Stochastic and Dynamic Games, Evolutionary Games, Repeated Games (C73), Stochastic Games
Abstract

We study stochastic games with an infinite horizon and sequential moves played by an arbitrary number of players. We assume that social memory is finite--every player, except possibly one, is finitely lived and cannot observe events that are sufficiently far back in the past. This class of games includes games between a long-run player and a sequence of short-run players, and games with overlapping generations of players. An equilibrium is purifiable if some close-by behaviour is consistent with equilibrium when agents' payoffs in each period are perturbed additively and independently. We show that only Markov equilibria are purifiable when social memory is finite. Thus if a game has at most one long-run player, all purifiable equilibria are Markov.

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