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On existence of ex post Nash consistent representation for effectivity functions

Author

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  • Hans Peters

    ()

  • Marc Schröder

    ()

  • Dries Vermeulen

    ()

Abstract

We consider effectivity functions for finitely many players and alternatives. We assume that players have incomplete information—with private values—about the preferences of the other players. Our main result is the characterization of effectivity functions which have an ex post Nash consistent representation, i.e., there is a game form such that (i) the distribution of power among coalitions of players is the same as in the effectivity function and (ii) there is an ex post Nash equilibrium (in pure strategies) for any preference profile. Copyright The Author(s) 2015

Suggested Citation

  • Hans Peters & Marc Schröder & Dries Vermeulen, 2015. "On existence of ex post Nash consistent representation for effectivity functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(2), pages 287-307, September.
  • Handle: RePEc:spr:sochwe:v:45:y:2015:i:2:p:287-307
    DOI: 10.1007/s00355-015-0891-6
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    References listed on IDEAS

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    1. Moulin, H. & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 115-145, June.
    2. Bergemann, Dirk & Morris, Stephen, 2008. "Ex post implementation," Games and Economic Behavior, Elsevier, vol. 63(2), pages 527-566, July.
    3. Peleg, Bezalel & Peters, Hans & Storcken, Ton, 2002. "Nash consistent representation of constitutions: a reaction to the Gibbard paradox," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 267-287, March.
    4. Boros, Endre & Elbassioni, Khaled & Gurvich, Vladimir & Makino, Kazuhisa, 2010. "On effectivity functions of game forms," Games and Economic Behavior, Elsevier, vol. 68(2), pages 512-531, March.
    5. Dirk Bergemann & Juuso Valimaki, 2002. "Information Acquisition and Efficient Mechanism Design," Econometrica, Econometric Society, vol. 70(3), pages 1007-1033, May.
    6. Philippe Jehiel & Moritz Meyer-ter-Vehn & Benny Moldovanu & William R. Zame, 2006. "The Limits of ex post Implementation," Econometrica, Econometric Society, vol. 74(3), pages 585-610, May.
    7. Bezalel Peleg & Shmuel Zamir, 2014. "Representation of constitutions under incomplete information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(2), pages 279-302, October.
    8. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
    9. Partha Dasgupta & Eric Maskin, 2000. "Efficient Auctions," The Quarterly Journal of Economics, Oxford University Press, vol. 115(2), pages 341-388.
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    11. Cremer, Jacques & McLean, Richard P, 1985. "Optimal Selling Strategies under Uncertainty for a Discriminating Monopolist When Demands Are Interdependent," Econometrica, Econometric Society, vol. 53(2), pages 345-361, March.
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    Cited by:

    1. Bezalel Peleg & Ron Holzman, 2017. "Representations of Political Power Structures by Strategically Stable Game Forms: A Survey," Games, MDPI, Open Access Journal, vol. 8(4), pages 1-17, October.

    More about this item

    Keywords

    C62; C70; D82;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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