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Non-cooperative bargaining in apex games and the kernel

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  • Montero, Maria

Abstract

This paper studies non-cooperative bargaining with random proposers in apex games. Two di¤erent protocols are considered: the egalitarian propocol, which selects each player to be the proposer with the same probability, and the proportional protocol, which selects each player with a probability proportional to his number of votes. Expected equilibrium payo¤s coincide with the kernel for the grand coalition regardless of the protocol. Expected payo¤s conditional on a coalition may depend on the protocol: given a coalition of the apex player with a minor player, an egalitarian protocol yields a nearly equal split whereas a proportional protocol leads to a proportional split.
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  • Montero, Maria, 2002. "Non-cooperative bargaining in apex games and the kernel," Games and Economic Behavior, Elsevier, vol. 41(2), pages 309-321, November.
    • Handle: RePEc:eee:gamebe:v:41:y:2002:i:2:p:309-321
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    Cited by:

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    2. Testa, Cecilia, 2003. "Government corruption and legislative procedures: is one chamber better than two?," LSE Research Online Documents on Economics 6642, London School of Economics and Political Science, LSE Library.
    3. Maria Montero, 2023. "Coalition Formation in Games with Externalities," Dynamic Games and Applications, Springer, vol. 13(2), pages 525-548, June.
    4. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 219-258, May.
    5. Maria Montero & Alex Possajennikov, 2021. "An Adaptive Model of Demand Adjustment in Weighted Majority Games," Games, MDPI, vol. 13(1), pages 1-17, December.
    6. Drouvelis, Michalis & Montero, Maria & Sefton, Martin, 2010. "Gaining power through enlargement: Strategic foundations and experimental evidence," Games and Economic Behavior, Elsevier, vol. 69(2), pages 274-292, July.
    7. Maria Montero, 2023. "Bargaining in Legislatures: A New Donation Paradox," Studies in Choice and Welfare, in: Sascha Kurz & Nicola Maaser & Alexander Mayer (ed.), Advances in Collective Decision Making, pages 159-171, Springer.
    8. Akira Okada, 2015. "Cooperation and Institution in Games," The Japanese Economic Review, Japanese Economic Association, vol. 66(1), pages 1-32, March.
    9. Maria Montero, 2010. "Bargaining in Legislatures: A New Donation Paradox," Discussion Papers 2010-19, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    10. Montero, M.P., 2002. "Two-Stage Bargaining with Reversible Coalitions : The Case of Apex Games," Discussion Paper 2002-26, Tilburg University, Center for Economic Research.
    11. Maria Montero, 2015. "A Model of Protocoalition Bargaining with Breakdown Probability," Games, MDPI, vol. 6(2), pages 1-18, April.
    12. Guillaume Fréchette & John H. Kagel & Massimo Morelli, 2005. "Behavioral Identification in Coalitional Bargaining: An Experimental Analysis of Demand Bargaining and Alternating Offers," Econometrica, Econometric Society, vol. 73(6), pages 1893-1937, November.
    13. Dominik Karos, 2012. "Coalition Formation in Generalized Apex Games," Working Papers 2012.38, Fondazione Eni Enrico Mattei.
    14. Gomes, Armando, 2015. "Multilateral negotiations and formation of coalitions," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 77-91.
    15. Okada, Akira & 岡田, 章, 2012. "The Stationary Equilibrium of Three-Person Cooperative Games: A Classification," Discussion Papers 2012-06, Graduate School of Economics, Hitotsubashi University.
    16. Dominik Karos, 2013. "Coalition Formation in General Apex Games," Economics Series Working Papers 680, University of Oxford, Department of Economics.
    17. Tobias Hiller, 2021. "Hierarchy and the size of a firm," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 68(3), pages 389-404, September.
    18. Tobias Hiller, 2018. "The Effects of Excluding Coalitions," Games, MDPI, vol. 9(1), pages 1-7, January.
    19. 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.
    20. Kristal K. Trejo & Ruben Juarez & Julio B. Clempner & Alexander S. Poznyak, 2023. "Non-Cooperative Bargaining with Unsophisticated Agents," Computational Economics, Springer;Society for Computational Economics, vol. 61(3), pages 937-974, March.
    21. Klaus Abbink, 2006. "Majority rip-off in referendum voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(1), pages 1-21, January.
    22. Michalis Drouvelis & Maria Montero & Martin Sefton, 2007. "The Paradox of New Members: Strategic Foundations and Experimental Evidence," Discussion Papers 2007-06, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    23. Karos, Dominik, 2014. "Coalition formation in general apex games under monotonic power indices," Games and Economic Behavior, Elsevier, vol. 87(C), pages 239-252.
    24. Joosung Lee, 2013. "Bargaining and Buyout," 2013 Papers ple701, Job Market Papers.
    25. Chih Chang & Cheng-Cheng Hu, 2017. "A non-cooperative interpretation of the kernel," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(1), pages 185-204, March.

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    More about this item

    JEL classification:

    • 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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