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The Stationary Equilibrium of Three-Person Cooperative Games: A Classification

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  • Okada, Akira

Abstract

We present a classification of all stationary subgame perfect equilibria of the random proposer model for a three-person cooperative game according to the level of efficiency. The efficiency level is characterized by the number of "central" players who join all equilibrium coalitions. The existence of a central player guarantees asymptotic efficiency. The marginal contributions of players to the grand coalition play a critical role in their expected equilibrium payoffs.

Suggested Citation

  • Okada, Akira, 2012. "The Stationary Equilibrium of Three-Person Cooperative Games: A Classification," Discussion Papers 2012-06, Graduate School of Economics, Hitotsubashi University.
  • Handle: RePEc:hit:econdp:2012-06
    as

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    File URL: http://hermes-ir.lib.hit-u.ac.jp/rs/bitstream/10086/23256/1/070econDP12-06.pdf
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    References listed on IDEAS

    as
    1. Okada, Akira, 1996. "A Noncooperative Coalitional Bargaining Game with Random Proposers," Games and Economic Behavior, Elsevier, vol. 16(1), pages 97-108, September.
    2. Montero, Maria, 2002. "Non-cooperative bargaining in apex games and the kernel," Games and Economic Behavior, Elsevier, vol. 41(2), pages 309-321, November.
    3. Olivier Compte & Philippe Jehiel, 2010. "The Coalitional Nash Bargaining Solution," Econometrica, Econometric Society, vol. 78(5), pages 1593-1623, September.
    4. Ray, Debraj, 2007. "A Game-Theoretic Perspective on Coalition Formation," OUP Catalogue, Oxford University Press, number 9780199207954.
    5. repec:cup:apsrev:v:83:y:1989:i:04:p:1181-1206_08 is not listed on IDEAS
    6. Daniel J. Seidmann & Eyal Winter, 1998. "A Theory of Gradual Coalition Formation," Review of Economic Studies, Oxford University Press, vol. 65(4), pages 793-815.
    7. Okada, Akira, 2011. "Coalitional bargaining games with random proposers: Theory and application," Games and Economic Behavior, Elsevier, vol. 73(1), pages 227-235, September.
    8. Montero, Maria, 2006. "Noncooperative foundations of the nucleolus in majority games," Games and Economic Behavior, Elsevier, vol. 54(2), pages 380-397, February.
    9. Okada, Akira, 2010. "The Nash bargaining solution in general n-person cooperative games," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2356-2379, November.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    cooperative game; noncooperative bargaining; three-person game; random proposer; core; marginal contribution;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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