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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.

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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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Bibliographic Info

Paper provided by Graduate School of Economics, Hitotsubashi University in its series Discussion Papers with number 2012-06.

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Length: 23 p.
Date of creation: Oct 2012
Date of revision:
Handle: RePEc:hit:econdp:2012-06

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

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  1. Olivier Compte & Philippe Jehiel, 2008. "The Coalitional Nash Bargaining Solution," Levine's Bibliography 122247000000001852, UCLA Department of Economics.
  2. Ray, Debraj, 2007. "A Game-Theoretic Perspective on Coalition Formation," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780199207954, October.
  3. Okada, Akira, 2007. "Coalitional Bargaining Games with Random Proposers: Theory and Application," Discussion Papers 2007-10, Graduate School of Economics, Hitotsubashi University.
  4. Montero, M.P., 1999. "Noncooperative Bargaining in Apex Games and the Kernel," Discussion Paper, Tilburg University, Center for Economic Research 1999-61, Tilburg University, Center for Economic Research.
  5. Montero, Maria, 2006. "Noncooperative foundations of the nucleolus in majority games," Games and Economic Behavior, Elsevier, Elsevier, vol. 54(2), pages 380-397, February.
  6. Okada, Akira, 1996. "A Noncooperative Coalitional Bargaining Game with Random Proposers," Games and Economic Behavior, Elsevier, Elsevier, vol. 16(1), pages 97-108, September.
  7. Okada, Akira, 2010. "The Nash bargaining solution in general n-person cooperative games," Journal of Economic Theory, Elsevier, Elsevier, vol. 145(6), pages 2356-2379, November.
  8. Seidmann, Daniel J & Winter, Eyal, 1998. "A Theory of Gradual Coalition Formation," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 65(4), pages 793-815, October.
  9. John F. Nash, 2008. "The Agencies Method For Modeling Coalitions And Cooperation In Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 539-564.
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