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Bargaining Sets of Voting Games

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  • Bezalel Peleg

    ()

  • Peter Sudholter

    ()

Abstract

Let A be a finite set of m ³ 3 alternatives, let N be a finite set of n ³ 3 players and let R n be a profile of linear preference orderings on A of the players. Throughout most of the paper the considered voting system is the majority rule. Let u N be a profile of utility functions for R N . Using a -effectiveness we define the NTU game V u N and investigate its Aumann-Davis-Maschler and Mas-Colell bargaining sets. The first bargaining set is nonempty for m = 3 and it may be empty for m ³ 4. Moreover, in a simple probabilistic model, for fixed m, the probability that the Aumann-Davis-Maschler bargaining set is nonempty tends to one if n tends to infinity. The Mas-Colell bargaining set is nonempty for m £ 5 and it may be empty for m ³ 6. Moreover, we prove the following startling result: The Mas-Colell bargaining set of any simple majority voting game derived from the k-th replication of R N is nonempty, provided that k ³ n + 2. We also compute the NTU games which are derived from choice by plurality voting and approval voting, and we analyze some interesting examples.

Suggested Citation

  • Bezalel Peleg & Peter Sudholter, 2004. "Bargaining Sets of Voting Games," Discussion Paper Series dp376, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp376
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    References listed on IDEAS

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    1. Mas-Colell, Andreu, 1989. "An equivalence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 129-139, April.
    2. Gaertner,Wulf, 2006. "Domain Conditions in Social Choice Theory," Cambridge Books, Cambridge University Press, number 9780521028745, May.
    3. Peleg, Bezalel & Sudholter, Peter, 2005. "On the non-emptiness of the Mas-Colell bargaining set," Journal of Mathematical Economics, Elsevier, vol. 41(8), pages 1060-1068, December.
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    Citations

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    Cited by:

    1. Guillermo Owen, 2010. "Michael Maschler’s bibliography," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 301-308, March.
    2. Adam Idzik & Gyula O.H. Katona & Rajiv Vohra, 1999. "Civil Conflict: Ended Or Never Ending?," Working Papers 99-33, Brown University, Department of Economics.
    3. Page Jr., Frank H. & Wooders, Myrna, 2009. "Strategic basins of attraction, the path dominance core, and network formation games," Games and Economic Behavior, Elsevier, vol. 66(1), pages 462-487, May.
    4. VAN STEENBERGHE, Vincent, 2004. "Core-stable and equitable allocations of greenhouse gas emission permits," CORE Discussion Papers 2004075, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Michel Grabisch & Peter Sudhölter, 2012. "The bounded core for games with precedence constraints," Annals of Operations Research, Springer, vol. 201(1), pages 251-264, December.
    6. Guni Orshan & Peter Sudhölter, 2010. "The positive core of a cooperative game," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 113-136, March.
    7. Yair Tauman & Andriy Zapechelnyuk, 2010. "On (non-) monotonicity of cooperative solutions," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 171-175, March.
    8. Michael Maschler & Jos Potters & Hans Reijnierse, 2010. "The nucleolus of a standard tree game revisited: a study of its monotonicity and computational properties," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 89-104, March.
    9. Khmelnitskaya, Anna B. & Sudhölter, Peter, 2011. "The prenucleolus for games with communication structures," Discussion Papers of Business and Economics 10/2011, University of Southern Denmark, Department of Business and Economics.
    10. Massimiliano Amarante & Luigi Montrucchio, 2010. "The bargaining set of a large game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(3), pages 313-349, June.
    11. Gooni Orshan & Peter Sudholter, 2001. "Reconfirming the Prenucleolus," Discussion Paper Series dp267, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    12. D. Granot & H. Hamers & J. Kuipers & M. Maschler, 2004. "Chinese Postman Games on a Class of Eulerian Graphs," Discussion Paper Series dp366, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    13. Wenbo Yang & Jiuqiang Liu & Xiaodong Liu, 2011. "Aubin cores and bargaining sets for convex cooperative fuzzy games," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(3), pages 467-479, August.
    14. Lloyd S. Shapley, 1992. "Kernels of Replicated Market Games," UCLA Economics Working Papers 654, UCLA Department of Economics.
    15. Massimiliano Amarante & Luigi Montrucchio, 2007. "Mas-Colell Bargaining Set of Large Games," Carlo Alberto Notebooks 63, Collegio Carlo Alberto.
    16. Josep M. Izquierdo & Carles Rafels, 2010. "On the coincidence between the Shimomuras bargaining sets and the core," Working Papers in Economics 241, Universitat de Barcelona. Espai de Recerca en Economia.

    More about this item

    Keywords

    NTU game; bargaining set; majority rule; plurality voting; approval voting;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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