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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.

Suggested Citation

  • Okada, Akira, 2007. "Coalitional Bargaining Games with Random Proposers: Theory and Application," Discussion Papers 2007-10, Graduate School of Economics, Hitotsubashi University.
  • Handle: RePEc:hit:econdp:2007-10
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    References listed on IDEAS

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    1. Okada, Akira, 1996. "A Noncooperative Coalitional Bargaining Game with Random Proposers," Games and Economic Behavior, Elsevier, vol. 16(1), pages 97-108, September.
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    13. Eraslan, Hulya & Merlo, Antonio, 2002. "Majority Rule in a Stochastic Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 103(1), pages 31-48, March.
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    Cited by:

    1. Elliott, M. & Nava, F., 2017. "Decentralized Bargaining in Matching Markets: Efficient Stationary Equilibria and the Core," Cambridge Working Papers in Economics 1742, Faculty of Economics, University of Cambridge.
    2. Arnold Polanski & Emiliya Lazarova, 2015. "Dynamic multilateral markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 815-833, November.
    3. Siddhartha Bandyopadhyay & Kalyan Chatterjee & Tomas Sjöström, 2013. "Pre-electoral Coalitions and Post-election Bargaining," World Scientific Book Chapters,in: Bargaining in the Shadow of the Market Selected Papers on Bilateral and Multilateral Bargaining, chapter 7, pages 129-181 World Scientific Publishing Co. Pte. Ltd..
    4. 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).
    5. Ray, Debraj & Vohra, Rajiv, 2015. "Coalition Formation," Handbook of Game Theory with Economic Applications, Elsevier.
    6. Eraslan, Hülya & McLennan, Andrew, 2013. "Uniqueness of stationary equilibrium payoffs in coalitional bargaining," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2195-2222.
    7. Sawa, Ryoji, 2014. "Stochastic stability in coalitional bargaining problems," MPRA Paper 58037, University Library of Munich, Germany, revised 11 May 2014.
    8. 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.
    9. Masanori Mitsutsune & Takanori Adachi, 2014. "Estimating noncooperative and cooperative models of bargaining: an empirical comparison," Empirical Economics, Springer, vol. 47(2), pages 669-693, September.
    10. Harold Houba & Gerard Laan & Yuyu Zeng, 2015. "International Environmental Agreements for River Sharing Problems," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 62(4), pages 855-872, December.
    11. Akira Okada, 2014. "The stationary equilibrium of three-person coalitional bargaining games with random proposers: a classification," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 953-973, November.
    12. Akira Okada, 2015. "Cooperation and Institution in Games," The Japanese Economic Review, Japanese Economic Association, vol. 66(1), pages 1-32, March.
    13. Akira Okada, 2018. "Non-cooperative Bargaining for Side Payments Contract," KIER Working Papers 983, Kyoto University, Institute of Economic Research.
    14. Elliott, Matt & Nava, Francesco, 2018. "Decentralized bargaining in matching markets: efficient stationary equilibria and the core," LSE Research Online Documents on Economics 87219, London School of Economics and Political Science, LSE Library.
    15. Breitmoser, Yves & Tan, Jonathan H.W., 2014. "Reference Dependent Altruism," MPRA Paper 52774, University Library of Munich, Germany.
    16. Tomohiko Kawamori, 2013. "Rejecter-proposer legislative bargaining with heterogeneous time and risk preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(1), pages 27-40, January.
    17. Ricardo Nieva, 2015. "The Coalitional Nash Bargaining Solution with Simultaneous Payoff Demands," Working Papers 2015.67, Fondazione Eni Enrico Mattei.
    18. Okada, Akira, 2012. "The Stationary Equilibrium of Three-Person Cooperative Games: A Classification," Discussion Papers 2012-06, Graduate School of Economics, Hitotsubashi University.
    19. Britz, Volker & Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2015. "Delay, multiplicity, and non-existence of equilibrium in unanimity bargaining games," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 192-202.

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