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Uniqueness of stationary equilibrium payoffs in coalitional bargaining

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  • Eraslan, Hülya
  • McLennan, Andrew

Abstract

We study a model of sequential bargaining in which, in each period before an agreement is reached, the proposerʼs identity is randomly determined, the proposer suggests a division of a pie of size one, each other agent either approves or rejects the proposal, and the proposal is implemented if the set of approving agents is a winning coalition for the proposer. The theory of the fixed point index is used to show that stationary equilibrium expected payoffs of this coalitional bargaining game are unique. This generalizes Eraslan [34] insofar as: (a) there are no restrictions on the structure of sets of winning coalitions; (b) different proposers may have different sets of winning coalitions; (c) there may be a positive probability that no proposer is selected.

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  • Eraslan, Hülya & McLennan, Andrew, 2013. "Uniqueness of stationary equilibrium payoffs in coalitional bargaining," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2195-2222.
  • Handle: RePEc:eee:jetheo:v:148:y:2013:i:6:p:2195-2222
    DOI: 10.1016/j.jet.2013.09.007
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    Cited by:

    1. Le Breton, Michel & Montero, Maria & Zaporozhets, Vera, 2012. "Voting power in the EU council of ministers and fair decision making in distributive politics," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 159-173.
    2. repec:eee:jetheo:v:171:y:2017:i:c:p:293-315 is not listed on IDEAS
    3. repec:eee:gamebe:v:107:y:2018:i:c:p:60-92 is not listed on IDEAS
    4. Maaser, Nicola & Traub, Stefan & Paetzel, Fabian, 2017. "Power illusion in coalitional bargaining: An experimental analysis," Annual Conference 2017 (Vienna): Alternative Structures for Money and Banking 168155, Verein für Socialpolitik / German Economic Association.
    5. Zaporozhets, Vera, 2015. "Power Distribution in French River Basin Committees," TSE Working Papers 15-558, Toulouse School of Economics (TSE).
    6. P. Jean-Jacques Herings & A. Predtetchinski, 2016. "Bargaining under monotonicity constraints," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(1), pages 221-243, June.
    7. Kalandrakis, Tasos, 2015. "Computation of equilibrium values in the Baron and Ferejohn bargaining model," Games and Economic Behavior, Elsevier, vol. 94(C), pages 29-38.
    8. Eraslan, Hülya & Merlo, Antonio, 2017. "Some unpleasant bargaining arithmetic?," Journal of Economic Theory, Elsevier, vol. 171(C), pages 293-315.
    9. Maria Montero, 2007. "The Paradox of New Members in the Council of Ministers: A Noncooperative Approach," Discussion Papers 2007-12, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    10. Le Breton, Michel & Van Der Straeten, Karine, 2017. "Alliances Electorales et Gouvernementales : La Contribution de la Théorie des Jeux Coopératifs à la Science Politique," TSE Working Papers 17-789, Toulouse School of Economics (TSE), revised Jun 2017.
    11. 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.
    12. Toshiji Miyakawa, 2009. "Existence and efficiency of a stationary subgame-perfect equilibrium in coalitional bargaining models with nonsuperadditive payoffs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(2), pages 291-306, May.
    13. 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.
    14. Akira Okada, 2015. "Cooperation and Institution in Games," The Japanese Economic Review, Japanese Economic Association, vol. 66(1), pages 1-32, March.
    15. Le Breton, Michel & Thomas, Alban & Zaporozhets, Vera, 2012. "Bargaining in River Basin Committees: Rules Versus Discretion," TSE Working Papers 12-324, Toulouse School of Economics (TSE).
    16. Hülya Eraslan, 2016. "Uniqueness of stationary equilibrium payoffs in the Baron–Ferejohn model with risk-averse players," International Journal of Economic Theory, The International Society for Economic Theory, vol. 12(1), pages 29-40, March.
    17. Jan Zapal, 2014. "Simple Markovian Equilibria in Dynamic Spatial Legislative Bargaining," CERGE-EI Working Papers wp515, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    18. Maria Montero, 2015. "A Model of Protocoalition Bargaining with Breakdown Probability," Games, MDPI, Open Access Journal, vol. 6(2), pages 1-18, April.
    19. Yves Breitmoser, 2011. "Parliamentary bargaining with priority recognition for committee members," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(1), pages 149-169, June.
    20. Ray, Debraj & Vohra, Rajiv, 2015. "Coalition Formation," Handbook of Game Theory with Economic Applications, Elsevier.
    21. Montero, Maria, 2017. "Proportional Payoffs in Legislative Bargaining with Weighted Voting: A Characterization," Quarterly Journal of Political Science, now publishers, vol. 12(3), pages 325-346, October.
    22. Joosung Lee, 2013. "Bargaining and Buyout," 2013 Papers ple701, Job Market Papers.
    23. Vincent Anesi & Daniel J Seidmann, 2012. "Bargaining in Standing Committees," Discussion Papers 2012-09, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    24. Kurz, Sascha & Napel, Stefan & Nohn, Andreas, 2014. "The nucleolus of large majority games," Economics Letters, Elsevier, vol. 123(2), pages 139-143.
    25. Miller, Luis & Montero, Maria & Vanberg, Christoph, 2018. "Legislative bargaining with heterogeneous disagreement values: Theory and experiments," Games and Economic Behavior, Elsevier, vol. 107(C), pages 60-92.

    More about this item

    Keywords

    Noncooperative bargaining; Multilateral bargaining; TU games; Simple games; Coalitions; Legislative bargaining; Fixed points; Fixed point index;

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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