IDEAS home Printed from https://ideas.repec.org/p/cla/levrem/122247000000000935.html
   My bibliography  Save this paper

Bargaining Sets of Majority Voting Games

Author

Listed:
  • Ron Holzman
  • Bezalel Peleg
  • Peter Sudholter

Abstract

Let A be a finite set of m alternatives, let N be a finite set of n players and let R N be a profile of linear preference orderings on A of the players. Let u N be a profile of utility functions for R N . We define the NTU game V u N that corresponds to simple majority voting, 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. However, 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. Furthermore, it may be empty even if we insist that n be odd, provided that m is sufficiently large. Nevertheless, we show that 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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Ron Holzman & Bezalel Peleg & Peter Sudholter, 2005. "Bargaining Sets of Majority Voting Games," Levine's Bibliography 122247000000000935, UCLA Department of Economics.
  • Handle: RePEc:cla:levrem:122247000000000935
    as

    Download full text from publisher

    File URL: http://ratio.huji.ac.il/dp/dp410.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Vohra, Rajiv, 1991. "An existence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 19-34.
    2. William Gehrlein, 2002. "Condorcet's paradox and the likelihood of its occurrence: different perspectives on balanced preferences ," Theory and Decision, Springer, vol. 52(2), pages 171-199, March.
    3. Mas-Colell, Andreu, 1989. "An equivalence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 129-139, April.
    4. Gaertner,Wulf, 2006. "Domain Conditions in Social Choice Theory," Cambridge Books, Cambridge University Press, number 9780521028745, February.
    5. Nechemia Asscher, 1976. "An Ordinal Bargaining Set for Games Without Side Payments," Mathematics of Operations Research, INFORMS, vol. 1(4), pages 381-389, November.
    6. Ron Holzman, 2001. "The comparability of the classical and the Mas-Colell bargaining sets," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(4), pages 543-553.
    7. Dutta, Bhaskar & Ray, Debraj & Sengupta, Kunal & Vohra, Rajiv, 1989. "A consistent bargaining set," Journal of Economic Theory, Elsevier, vol. 49(1), pages 93-112, October.
    8. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Roland Pongou & Lawrence Diffo Lambo & Bertrand Tchantcho, 2008. "Cooperation, stability and social welfare under majority rule," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(3), pages 555-574, June.
    2. Bezalel Peleg & Peter Sudhölter, 2015. "On Bargaining Sets of Convex NTU Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 17(04), pages 1-7.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Massimiliano Amarante & Luigi Montrucchio, 2007. "Mas-Colell Bargaining Set of Large Games," Carlo Alberto Notebooks 63, Collegio Carlo Alberto.
    2. Roberto Serrano & Rajiv Vohra, 2002. "Implementing the Mas-Colell bargaining set," Investigaciones Economicas, Fundación SEPI, vol. 26(2), pages 285-298, May.
    3. José-Manuel Giménez-Gómez & Cori Vilella, 2015. "On the Coincidence of the Mas-Colell Bargaining Set and the Core," Journal of Social Economics, Research Academy of Social Sciences, vol. 2(3), pages 117-121.
    4. Hervés-Estévez, Javier & Moreno-García, Emma, 2018. "Bargaining set with endogenous leaders: A convergence result," Economics Letters, Elsevier, vol. 166(C), pages 10-13.
    5. Serrano, Roberto & Vohra, Rajiv, 2002. "Bargaining and Bargaining Sets," Games and Economic Behavior, Elsevier, vol. 39(2), pages 292-308, May.
    6. Perez-Castrillo, David & Wettstein, David, 2000. "Implementation of Bargaining Sets via Simple Mechanisms," Games and Economic Behavior, Elsevier, vol. 31(1), pages 106-120, April.
    7. 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.
    8. Michel Le Breton & Karine Van Der Straeten, 2017. "Alliances Électorales et Gouvernementales : La Contribution de la Théorie des Jeux Coopératifs à la Science Politique," Revue d'économie politique, Dalloz, vol. 127(4), pages 637-736.
    9. 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.
    10. 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.
    11. Serrano, Roberto, 1997. "A comment on the Nash program and the theory of implementation," Economics Letters, Elsevier, vol. 55(2), pages 203-208, August.
    12. Einy, Ezra & Holzman, Ron & Monderer, Dov & Shitovitz, Benyamin, 1997. "Core Equivalence Theorems for Infinite Convex Games," Journal of Economic Theory, Elsevier, vol. 76(1), pages 1-12, September.
    13. Bezalel Peleg & Peter Sudhölter, 2015. "On Bargaining Sets of Convex NTU Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 17(04), pages 1-7.
    14. Javier Hervés-Estévez & Emma Moreno-García, 2018. "A limit result on bargaining sets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(2), pages 327-341, August.
    15. Elena Iñarra & Roberto Serrano & Ken-Ichi Shimomura, 2020. "The Nucleolus, the Kernel, and the Bargaining Set: An Update," Revue économique, Presses de Sciences-Po, vol. 71(2), pages 225-266.
    16. Graziano, Maria Gabriella & Pesce, Marialaura & Urbinati, Niccolò, 2020. "Generalized coalitions and bargaining sets," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 80-89.
    17. Jesús Getán & Josep Izquierdo & Jesús Montes & Carles Rafels, 2015. "The bargaining set for almost-convex games," Annals of Operations Research, Springer, vol. 225(1), pages 83-89, February.
    18. Einy, Ezra & Holzman, Ron & Monderer, Dov, 1999. "On the Least Core and the Mas-Colell Bargaining Set," Games and Economic Behavior, Elsevier, vol. 28(2), pages 181-188, August.
    19. Hu, Cheng-Cheng, 2010. "A noncooperative approach to the Mas-Colell bargaining set," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 884-892, September.
    20. 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.

    More about this item

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cla:levrem:122247000000000935. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: http://www.dklevine.com/ .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: David K. Levine (email available below). General contact details of provider: http://www.dklevine.com/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.