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Coalitional Bargaining Games with Random Proposers: Theory and Application

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  • Okada, Akira

Abstract

We consider a noncooperative coalitional bargaining game with random proposers. In a general case that the recognition probability is arbitrary andplayers have different discount factors for future payoffs, the existence of a stationary subgame perfect equilibrium (SSPE) is proved, and the condition for the grand coalition to be formed is provided. We also prove that the grand-coalition SSPE is a unique symmetric SSPE for any discount factor in a symmetric game with nonempty core. In the last part of the paper, we apply the bargaining model to a production economy with one employer and multiple workers. When players are sufficiently patient, the economy has a unique SSPE payoff. The equilibrium allocation is compared with cooperative solutions such as the core, the Shapley value and the nucleolus. The SSPE payoff and the nucleolus have similar distributional properties.

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File URL: http://hermes-ir.lib.hit-u.ac.jp/rs/bitstream/10086/16934/1/070econDP07-10.pdf
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Bibliographic Info

Paper provided by Graduate School of Economics, Hitotsubashi University in its series Discussion Papers with number 2007-10.

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Length: 47 p.
Date of creation: Sep 2007
Date of revision:
Handle: RePEc:hit:econdp:2007-10

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  1. Okada, Akira, 1996. "A Noncooperative Coalitional Bargaining Game with Random Proposers," Games and Economic Behavior, Elsevier, Elsevier, vol. 16(1), pages 97-108, September.
  2. Montero, Maria, 2006. "Noncooperative foundations of the nucleolus in majority games," Games and Economic Behavior, Elsevier, Elsevier, vol. 54(2), pages 380-397, February.
  3. Norman, Peter, 2002. "Legislative Bargaining and Coalition Formation," Journal of Economic Theory, Elsevier, Elsevier, vol. 102(2), pages 322-353, February.
  4. Ray, Debraj, 2007. "A Game-Theoretic Perspective on Coalition Formation," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780199207954, October.
  5. Armando Gomes, 2005. "Multilateral Contracting with Externalities," Econometrica, Econometric Society, Econometric Society, vol. 73(4), pages 1329-1350, 07.
  6. Stole, Lars A & Zwiebel, Jeffrey, 1996. "Intra-firm Bargaining under Non-binding Contracts," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 63(3), pages 375-410, July.
  7. Laruelle, Annick & Valenciano, Federico, 2008. "Noncooperative foundations of bargaining power in committees and the Shapley-Shubik index," Games and Economic Behavior, Elsevier, Elsevier, vol. 63(1), pages 341-353, May.
  8. Eraslan, H. & Merlo, A., 2000. "Majority Rule in a Stochastic Model of Bargaining," Working Papers, C.V. Starr Center for Applied Economics, New York University 00-05, C.V. Starr Center for Applied Economics, New York University.
  9. Armo Gomes & Philippe Jehiel, 2001. "Dynamic Processes of Social and Economic Interactions: On the Persistence of Inefficiencies," Penn CARESS Working Papers, Penn Economics Department 76ff153ae29996d16c454e473, Penn Economics Department.
  10. Olivier Compte & Philippe Jehiel, 2010. "The Coalitional Nash Bargaining Solution," Econometrica, Econometric Society, Econometric Society, vol. 78(5), pages 1593-1623, 09.
  11. Westermark, Andreas, 2003. "Bargaining, binding contracts, and competitive wages," Games and Economic Behavior, Elsevier, Elsevier, vol. 43(2), pages 296-311, May.
  12. Montero, Maria, 2002. "Non-cooperative bargaining in apex games and the kernel," Games and Economic Behavior, Elsevier, Elsevier, vol. 41(2), pages 309-321, November.
  13. Baron David & Kalai Ehud, 1993. "The Simplest Equilibrium of a Majority-Rule Division Game," Journal of Economic Theory, Elsevier, Elsevier, vol. 61(2), pages 290-301, December.
  14. Shaked, Avner & Sutton, John, 1984. "Involuntary Unemployment as a Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, Econometric Society, vol. 52(6), pages 1351-64, November.
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Cited by:
  1. Andrew McLennan & Hülya Eraslan, 2010. "Uniqueness of Stationary Equilibrium Payoffs in Coalitional Bargaining," Economics Working Paper Archive, The Johns Hopkins University,Department of Economics 562, The Johns Hopkins University,Department of Economics.
  2. Breitmoser, Yves & Tan, Jonathan H.W., 2014. "Reference Dependent Altruism," MPRA Paper 52774, University Library of Munich, Germany.
  3. Okada, Akira, 2012. "The Stationary Equilibrium of Three-Person Cooperative Games: A Classification," Discussion Papers, Graduate School of Economics, Hitotsubashi University 2012-06, Graduate School of Economics, Hitotsubashi University.
  4. Britz, Volker & Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2014. "On the convergence to the Nash bargaining solution for action-dependent bargaining protocols," Games and Economic Behavior, Elsevier, Elsevier, vol. 86(C), pages 178-183.
  5. Bandyopadhyay, Siddhartha & Chatterjee, Kalyan & Sj�str�m, Tomas, 2011. "Pre-electoral Coalitions and Post-election Bargaining," International Quarterly Journal of Political Science, now publishers, now publishers, vol. 6(1), pages 1-53, August.
  6. Tomohiko Kawamori, 2013. "Rejecter-proposer legislative bargaining with heterogeneous time and risk preferences," Social Choice and Welfare, Springer, Springer, vol. 40(1), pages 27-40, January.
  7. Harold Houba & Gerard van der Laan, 2013. "International Environmental Agreements for River Sharing Problems," Tinbergen Institute Discussion Papers, Tinbergen Institute 13-157/II, Tinbergen Institute.
  8. Herings P. Jean-Jacques & Britz Volker & Predtetchinski Arkadi, 2012. "On the Convergence to Nash Bargaining Solution for Endogenous Bargaining Protocols," Research Memorandum, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR) 030, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

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