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

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  • V. Bhaskar
  • George J. Mailath
  • Stephen Morris

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. Copyright 2013, Oxford University Press.

Suggested Citation

  • V. Bhaskar & George J. Mailath & Stephen Morris, 2013. "A Foundation for Markov Equilibria in Sequential Games with Finite Social Memory -super-," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(3), pages 925-948.
    • Handle: RePEc:oup:restud:v:80:y:2013:i:3:p:925-948
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    File URL: http://hdl.handle.net/10.1093/restud/rds047
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    Cited by:

    1. Kimmo Berg & Gijs Schoenmakers, 2017. "Construction of Subgame-Perfect Mixed-Strategy Equilibria in Repeated Games," Games, MDPI, vol. 8(4), pages 1-14, November.
    2. Harstad, Bård, 2021. "A Theory of Pledge-and-Review Bargaining," Memorandum 5/2022, Oslo University, Department of Economics, revised 21 Jun 2021.
    3. Sperisen, Benjamin, 2018. "Bounded memory and incomplete information," Games and Economic Behavior, Elsevier, vol. 109(C), pages 382-400.
    4. Houba, Harold & Wen, Quan, 2014. "Backward induction and unacceptable offers," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 151-156.
    5. Elliott, M. & Nava, F., 2017. "Decentralized Bargaining in Matching Markets: Efficient Stationary Equilibria and the Core," Cambridge Working Papers in Economics 1742, Faculty of Economics, University of Cambridge.
    6. Harstad, Bård, 2023. "Pledge-and-review bargaining," Journal of Economic Theory, Elsevier, vol. 207(C).
    7. Kováč, Eugen & Schmidt, Robert C., 2014. "Market share dynamics in a duopoly model with word-of-mouth communication," Games and Economic Behavior, Elsevier, vol. 83(C), pages 178-206.
    8. Elliott, Matthew L. & Nava, Francesco, 2019. "Decentralized bargaining in matching markets: efficient stationary equilibria and the core," Theoretical Economics, Econometric Society, vol. 14(1), January.
    9. P. Jean-Jacques Herings & Harold Houba, 2022. "Costless delay in negotiations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(1), pages 69-93, July.
    10. Benjamin Sperisen, 2018. "Bad Reputation Under Bounded And Fading Memory," Economic Inquiry, Western Economic Association International, vol. 56(1), pages 138-157, January.
    11. Morris, Stephen, 2014. "Coordination, timing and common knowledge," Research in Economics, Elsevier, vol. 68(4), pages 306-314.
    12. Marina Azzimonti & Laura Karpuska & Gabriel Mihalache, 2020. "Bargaining over Mandatory Spending and Entitlements," Department of Economics Working Papers 20-02, Stony Brook University, Department of Economics.
    13. Sugaya, Takuo & Takahashi, Satoru, 2013. "Coordination failure in repeated games with private monitoring," Journal of Economic Theory, Elsevier, vol. 148(5), pages 1891-1928.
    14. Christoph Diehl & Christoph Kuzmics, 2021. "The (non-)robustness of influential cheap talk equilibria when the sender’s preferences are state independent," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(4), pages 911-925, December.
    15. Attila Ambrus & Shih En Lu, 2015. "A Continuous-Time Model of Multilateral Bargaining," American Economic Journal: Microeconomics, American Economic Association, vol. 7(1), pages 208-249, February.
    16. Elliott, Matt & Nava, Francesco, 2019. "Decentralized bargaining in matching markets: efficient stationary equilibria and the core," LSE Research Online Documents on Economics 87219, London School of Economics and Political Science, LSE Library.
    17. Herings, P. Jean-Jacques & Meshalkin, Andrey & Predtetchinski, Arkadi, 2017. "A one-period memory folk theorem for multilateral bargaining games," Games and Economic Behavior, Elsevier, vol. 103(C), pages 185-198.
    18. Thomas Wiseman, 2015. "A Note on the Essentiality of Money under Limited Memory," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 18(4), pages 881-893, October.
    19. Wioletta Dziuda & Antoine Loeper, 2016. "Dynamic Collective Choice with Endogenous Status Quo," Journal of Political Economy, University of Chicago Press, vol. 124(4), pages 1148-1186.
    20. Ambrus, Attila & Greiner, Ben & Pathak, Parag A., 2015. "How individual preferences are aggregated in groups: An experimental study," Journal of Public Economics, Elsevier, vol. 129(C), pages 1-13.
    21. Marina Azzimonti & Gabriel P. Mihalache & Laura Karpuska, 2020. "Bargaining over Taxes and Entitlements," NBER Working Papers 27595, National Bureau of Economic Research, Inc.
    22. Heller, Yuval & Mohlin, Erik, 2015. "Unique Stationary Behavior," MPRA Paper 66179, University Library of Munich, Germany.
    23. Arieli, Itai & Koren, Moran & Smorodinsky, Rann, 2022. "The implications of pricing on social learning," Theoretical Economics, Econometric Society, vol. 17(4), November.
    24. Benjamin Sperisen, 2016. "Bounded Memory, Reputation, and Impatience," Working Papers 1602, Tulane University, Department of Economics.

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