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A Folk Theorem for Bargaining Games

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  • Herings P.J.J.
  • Meshalkin A.
  • Predtetchinski A.

    (METEOR)

Abstract

We study strategies with one–period recall in the context of a general class of multilateralbargaining games. A strategy has one–period recall if actions in a particular period are onlyconditioned on information in the previous and the current period. We show that if players aresufficiently patient, given any proposal in the space of possible agreements, there exists asubgame perfect equilibrium such that the given proposal is made and unanimously accepted inperiod zero. Our strategies are pure and have one–period recall, and we do not make use of apublic randomization device. The players’ discount factors are allowed to be heterogeneous.

Suggested Citation

  • Herings P.J.J. & Meshalkin A. & Predtetchinski A., 2012. "A Folk Theorem for Bargaining Games," Research Memorandum 056, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  • Handle: RePEc:unm:umamet:2012056
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    File URL: https://cris.maastrichtuniversity.nl/portal/files/1587761/content
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    References listed on IDEAS

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    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2010. "One-dimensional bargaining with Markov recognition probabilities," Journal of Economic Theory, Elsevier, vol. 145(1), pages 189-215, January.
    3. Fudenberg, Drew & Yamamoto, Yuichi, 2011. "The folk theorem for irreducible stochastic games with imperfect public monitoring," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1664-1683, July.
    4. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, August.
    5. Kalyan Chatterjee & Bhaskar Dutia & Debraj Ray & Kunal Sengupta, 2013. "A Noncooperative Theory of Coalitional Bargaining," World Scientific Book Chapters, in: Bargaining in the Shadow of the Market Selected Papers on Bilateral and Multilateral Bargaining, chapter 5, pages 97-111, World Scientific Publishing Co. Pte. Ltd..
    6. James W. Friedman, 1971. "A Non-cooperative Equilibrium for Supergames," Review of Economic Studies, Oxford University Press, vol. 38(1), pages 1-12.
    7. Haller, Hans, 1986. "Non-cooperative bargaining of N [ges] 3 players," Economics Letters, Elsevier, vol. 22(1), pages 11-13.
    8. Merlo, Antonio & Wilson, Charles A, 1995. "A Stochastic Model of Sequential Bargaining with Complete Information," Econometrica, Econometric Society, vol. 63(2), pages 371-399, March.
    9. Tasos Kalandrakis, 2006. "Regularity of pure strategy equilibrium points in a class of bargaining games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(2), pages 309-329, June.
    10. Binmore, Ken & Osborne, Martin J. & Rubinstein, Ariel, 1992. "Noncooperative models of bargaining," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 7, pages 179-225, Elsevier.
    11. V. Bhaskar & George J. Mailath & Stephen Morris, 2009. "A Foundation for Markov Equilibria in Infinite Horizon Perfect Information Games," PIER Working Paper Archive 09-029, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    12. Johannes Hörner & Wojciech Olszewski, 2009. "How Robust is the Folk Theorem?," The Quarterly Journal of Economics, Oxford University Press, vol. 124(4), pages 1773-1814.
    13. Drew Fudenberg & Eric Maskin, 2008. "The Folk Theorem In Repeated Games With Discounting Or With Incomplete Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 11, pages 209-230, World Scientific Publishing Co. Pte. Ltd..
    14. Ehud Lehrer & Ady Pauzner, 1999. "Repeated Games with Differential Time Preferences," Econometrica, Econometric Society, vol. 67(2), pages 393-412, March.
    15. Rubinstein, Ariel, 1979. "Equilibrium in supergames with the overtaking criterion," Journal of Economic Theory, Elsevier, vol. 21(1), pages 1-9, August.
    16. Banks, Jeffrey s. & Duggan, John, 2000. "A Bargaining Model of Collective Choice," American Political Science Review, Cambridge University Press, vol. 94(1), pages 73-88, March.
    17. Chen, Bo, 2008. "On effective minimax payoffs and unequal discounting," Economics Letters, Elsevier, vol. 100(1), pages 105-107, July.
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    Cited by:

    1. 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.

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