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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. 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.
  2. Norman, Peter, 2002. "Legislative Bargaining and Coalition Formation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 322-353, February.
  3. Armando Gomes & Philippe Jehiel, 2005. "Dynamic Processes of Social and Economic Interactions: On the Persistence of Inefficiencies," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 113(3), pages 626-667, June.
  4. Westermark, Andreas, 2003. "Bargaining, binding contracts, and competitive wages," Games and Economic Behavior, Elsevier, vol. 43(2), pages 296-311, May.
  5. 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.
  6. Montero, Maria, 2006. "Noncooperative foundations of the nucleolus in majority games," Games and Economic Behavior, Elsevier, vol. 54(2), pages 380-397, February.
  7. 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.
  8. Okada, Akira, 1996. "A Noncooperative Coalitional Bargaining Game with Random Proposers," Games and Economic Behavior, Elsevier, vol. 16(1), pages 97-108, September.
  9. Olivier Compte & Philippe Jehiel, 2008. "The Coalitional Nash Bargaining Solution," Levine's Bibliography 122247000000001852, UCLA Department of Economics.
  10. 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.
  11. Baron David & Kalai Ehud, 1993. "The Simplest Equilibrium of a Majority-Rule Division Game," Journal of Economic Theory, Elsevier, vol. 61(2), pages 290-301, December.
  12. Ray, Debraj, 2007. "A Game-Theoretic Perspective on Coalition Formation," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780199207954, October.
  13. Armando Gomes, 2005. "Multilateral Contracting with Externalities," Econometrica, Econometric Society, Econometric Society, vol. 73(4), pages 1329-1350, 07.
  14. Laruelle, Annick & Valenciano, Federico, 2008. "Noncooperative foundations of bargaining power in committees and the Shapley-Shubik index," Games and Economic Behavior, Elsevier, vol. 63(1), pages 341-353, May.
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Cited by:
  1. Andrew McLennan & Hülya Eraslan, 2010. "Uniqueness of Stationary Equilibrium Payoffs in Coalitional Bargaining," Economics Working Paper Archive 562, The Johns Hopkins University,Department of Economics.
  2. Okada, Akira, 2012. "The Stationary Equilibrium of Three-Person Cooperative Games: A Classification," Discussion Papers 2012-06, Graduate School of Economics, Hitotsubashi University.
  3. Harold Houba & Gerard van der Laan, 2013. "International Environmental Agreements for River Sharing Problems," Tinbergen Institute Discussion Papers 13-157/II, Tinbergen Institute.
  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, vol. 86(C), pages 178-183.
  5. Herings P. Jean-Jacques & Britz Volker & Predtetchinski Arkadi, 2012. "On the Convergence to Nash Bargaining Solution for Endogenous Bargaining Protocols," Research Memorandum 030, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  6. Bandyopadhyay, Siddhartha & Chatterjee, Kalyan & Sj�str�m, Tomas, 2011. "Pre-electoral Coalitions and Post-election Bargaining," Quarterly Journal of Political Science, now publishers, vol. 6(1), pages 1-53, August.
  7. Breitmoser, Yves & Tan, Jonathan H.W., 2014. "Reference Dependent Altruism," MPRA Paper 52774, University Library of Munich, Germany.
  8. 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.

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