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

• Published in: The Review of economic studies Vol. 80; no. 3 (284); pp. 925 - 948
• Main Authors: BHASKAR, V., MAILATH, GEORGE J., MORRIS, STEPHEN
• Format: Journal Article
• Language: English
• Published: Oxford Oxford University Press 01-07-2013
• Subjects: Chain stores; Dynamic games; Economic behaviour; Economic equilibrium; Economic models; Economic theory; Equilibrium; Game theory; Incumbents; Markov analysis; Markovian processes; Memory; Mixed strategy; Nash equilibrium; Repeated games; Stochastic games; Stochastic models; Stochastic processes; Studies
• ISSN: 0034-6527; 1467-937X
• DOI: 10.1093/restud/rds047

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.