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Representation of Effectivity Functions in Coalition Proof Nash Equilibrium: A Complete Characterization

Author

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  • Hans Keiding

    (Institute of Economics, University of Copenhagen)

  • Bezalel Peleg

    (Hebrew University of Jerusalem)

Abstract

The concept of coalition proof Nash equilibrium was introduced by Bernheim, Peleg, and Whinston [1987]. In the present paper, we consider the representation problem for coalition proof Nash equilibrium: For a given effectivity function, describing the power structure or the system of rights of coalitions in society, it is investigated whether there is a game form which gives rise to this effectivity function and which is such that for any preference assignment, there is a coalition proof Nash equilibrium. It is shown that the effectivity functions which can be represented in coalition proof Nash equilibrium are exactly those which satisfy the well-known properties of maximality and superadditivity. As a corollary of the result, we obtain necessary conditions for implementation of a social choice correspondence in coalition proof Nash equilibrium which can be formulated in terms of the associated effectivity function.

Suggested Citation

  • Hans Keiding & Bezalel Peleg, 1999. "Representation of Effectivity Functions in Coalition Proof Nash Equilibrium: A Complete Characterization," Discussion Papers 99-21, University of Copenhagen. Department of Economics.
  • Handle: RePEc:kud:kuiedp:9921
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    File URL: http://www.econ.ku.dk/english/research/publications/wp/1999/9921.pdf/
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    Cited by:

    1. Margarita Kirneva & Matias Nunez, 2021. "Voting by Simultaneous Vetoes," Working Papers 2021-08, Center for Research in Economics and Statistics.
    2. Hans Keiding & Bezalel Peleg, 2006. "Binary effectivity rules," Review of Economic Design, Springer;Society for Economic Design, vol. 10(3), pages 167-181, December.
    3. Keiding, Hans & Peleg, Bezalel, 2006. "On the continuity of representations of effectivity functions," Journal of Mathematical Economics, Elsevier, vol. 42(7-8), pages 827-842, November.
    4. Sinan Ertemel & Levent Kutlu & M. Remzi Sanver, 2015. "Voting games of resolute social choice correspondences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(1), pages 187-201, June.
    5. Peleg, Bezalel, 2004. "Representation of effectivity functions by acceptable game forms: a complete characterization," Mathematical Social Sciences, Elsevier, vol. 47(3), pages 275-287, May.

    More about this item

    Keywords

    effectivity functions; representation; coalition proof; Nash equilibrium;
    All these keywords.

    JEL classification:

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

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