A Foundation for Markov Equilibria with Finite Social Memory

31 Pages Posted: 6 Feb 2012

See all articles by V. Bhaskar

V. Bhaskar

University College London

George J. Mailath

University of Pennsylvania - Department of Economics; Research School of Economics, ANU

Stephen Morris

MIT

Date Written: January 31, 2012

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. Indeed, any stochastic game with infinitely lived players can be reinterpreted as one with finitely lived players: Each finitely-lived player is replaced by a successor, and receives the value of the successor's payoff. This value may arise from altruism, but the player also receives such a value if he can “sell” his position in a competitive market. In both cases, his objective will be to maximize infinite horizon payoffs, though his information on past events will be limited. An equilibrium is purifiable if close-by behavior 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.

Keywords: Purification, Markov perfect equilibrium, dynamic games

JEL Classification: C72, C73

Suggested Citation

Bhaskar, V. and Mailath, George J. and Morris, Stephen Edward, A Foundation for Markov Equilibria with Finite Social Memory (January 31, 2012). PIER Working Paper No. 12-003, Economic Theory Center Working Paper No. 31-2012, Available at SSRN: https://ssrn.com/abstract=1998810 or http://dx.doi.org/10.2139/ssrn.1998810

V. Bhaskar

University College London ( email )

Gower Street
London
United Kingdom

George J. Mailath (Contact Author)

University of Pennsylvania - Department of Economics ( email )

Ronald O. Perelman Center for Political Science
133 South 36th Street
Philadelphia, PA 19104-6297
United States
215-898-7908 (Phone)
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HOME PAGE: http://web.sas.upenn.edu/gmailath/

Research School of Economics, ANU ( email )

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Australia

Stephen Edward Morris

MIT ( email )

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Cambridge, MA 02139-4307
United States

HOME PAGE: http://https://economics.mit.edu/faculty/semorris

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