A Foundation for Markoiv Equilibria in Infinite Horizon Perfect Information Games

30 Pages Posted: 24 Aug 2009

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: August 5, 2009

Abstract

We study perfect information games with an infinite horizon played by an arbitrary number of players. This class of games includes infinitely repeated perfect information games, repeated games with asynchronous moves, games with long and short run players, games with overlapping generations of players, and canonical non-cooperative models of bargaining. We consider two restrictions on equilibria. An equilibrium is purifiable if close by behavior is consistent with equilibrium when agents' payoffs at each node are perturbed additively and independently. An equilibrium has bounded recall if there exists K such that at most one player's strategy depends on what happened more than K periods earlier. We show that only Markov equilibria have bounded memory and are purifiable. Thus if a game has at most one long-run player, all purifiable equilibria are Markov.

Keywords: Markov, bounded recall, purification

JEL Classification: C72, C73

Suggested Citation

Bhaskar, V. and Mailath, George J. and Morris, Stephen Edward, A Foundation for Markoiv Equilibria in Infinite Horizon Perfect Information Games (August 5, 2009). PIER Working Paper No. 09-029, Available at SSRN: https://ssrn.com/abstract=1460780 or http://dx.doi.org/10.2139/ssrn.1460780

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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