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A Foundation for Markov Equilibria with Finite Social Memory

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  • V. Bhaskar

    ()
    (University College London)

  • George J. Mailath

    ()
    (Department of Economics, University of Pennsylvania)

  • Stephen Morris

    ()
    (Department of Economics, Princeton University)

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.

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Bibliographic Info

Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 12-003.

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Length: 28 pages
Date of creation: 31 Jan 2012
Date of revision:
Handle: RePEc:pen:papers:12-003

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Keywords: Purification; Markov perfect equilibrium; dynamic games;

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  1. George Mailath & Wojciech Olszewski, 2008. "Folk theorems with Bounded Recall under(Almost) Perfect Monitoring," Discussion Papers 1462, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Eaton, Jonathan & Engers, Maxim, 1990. "Intertemporal Price Competition," Econometrica, Econometric Society, vol. 58(3), pages 637-59, May.
  3. Doraszelski, Ulrich & Escobar, Juan, 2008. "A Theory of Regular Markov Perfect Equilibria in Dynamic Stochastic Games: Genericity, Stability, and Purification," CEPR Discussion Papers 6805, C.E.P.R. Discussion Papers.
  4. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, September.
  5. Liu, Qingmin & Skrzypacz, Andrzej, 2009. "Limited Records and Reputation," Research Papers 2030, Stanford University, Graduate School of Business.
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