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Proportional Payoffs in Majority Games

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  • Maria Montero

    (School of Economics, University of Nottingham)

Abstract

This paper extends the Baron-Ferejohn model of legislative bargaining to general weighted majority games with two modifications: first, payoff division can only be agreed upon after the coalition has formed (two-stage bargaining); second, negotiations in the coalition can break down, in which case a new coalition may be formed (reversible coalitions). Under the most natural bargaining protocol, both expected payoffs and actual payoff division are proportional to the voting weights provided that the set of winning coalitions of minimum weight is weakly balanced and that the breakdown probability tends to 0. Homogeneity of the voting weights is neither necessary nor sufficient for proportional payoffs. Intermediate values of the breakdown probability produce predictions consistent with the empirical evidence on portfolio allocation in Europe: a moderate propoper advantage and a linear relationship between weights and ex post payoffs for all coalition members other than the proposer.

Suggested Citation

  • Maria Montero, 2008. "Proportional Payoffs in Majority Games," Discussion Papers 2008-03, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    • Handle: RePEc:not:notcdx:2008-03
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    File URL: https://www.nottingham.ac.uk/cedex/documents/papers/2008-03.pdf
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    References listed on IDEAS

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    4. Stephen Ansolabehere & James M. Snyder & Aaron B. Strauss & Michael M. Ting, 2005. "Voting Weights and Formateur Advantages in the Formation of Coalition Governments," American Journal of Political Science, John Wiley & Sons, vol. 49(3), pages 550-563, July.
    5. 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.
    6. Daniel Diermeier & Hulya Eraslan & Antonio Merlo, 2003. "A Structural Model of Government Formation," Econometrica, Econometric Society, vol. 71(1), pages 27-70, January.
    7. Michalis Drouvelis & Maria Montero & Martin Sefton, 2007. "The Paradox of New Members: Strategic Foundations and Experimental Evidence," Discussion Papers 2007-13, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    8. Diermeier, Daniel & Merlo, Antonio, 2004. "An empirical investigation of coalitional bargaining procedures," Journal of Public Economics, Elsevier, vol. 88(3-4), pages 783-797, March.
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    Cited by:

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    4. Marco Battaglini, 2021. "Coalition Formation in Legislative Bargaining," Journal of Political Economy, University of Chicago Press, vol. 129(11), pages 3206-3258.

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    More about this item

    Keywords

    coalition formation; legislative bargaining; weighted majority games; proportional payoffs; reversible coalitions;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • 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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