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Nash Consistent Representation of Effectivity Functions through Lottery Models

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  • Bezalel Peleg

    ()

  • Hans Peters

    ()

Abstract

Effectivity functions for finitely many players and alternatives are considered. It is shown that every monotonic and superadditive effectivity function can be augmented with equal chance lotteries to a finite lottery model - i.e., an effectivity function that preserves the original effectivity in terms of supports of lotteries - which has a Nash consistent representation. In other words, there exists a finite game form which represents the lottery model and which has a Nash equilibrium for any profile of utility functions, where lotteries are evaluated by their expected utility. No additional condition on the original effectivity function is needed.

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Bibliographic Info

Paper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp404.

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Length: 16 pages
Date of creation: Sep 2005
Date of revision:
Publication status: Forthcoming in Games and Economic Behavior.
Handle: RePEc:huj:dispap:dp404

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  1. Wulf Gaerther & Prasanta K. Pattanaik & Kotaro Suzumura, 1991. "Individual Rights Revisited," Discussion Paper Series a238, Institute of Economic Research, Hitotsubashi University.
    • Gaertner, Wulf & Pattanaik, Prasanta K & Suzumura, Kotaro, 1992. "Individual Rights Revisited," Economica, London School of Economics and Political Science, vol. 59(234), pages 161-77, May.
  2. Moulin, Hervé & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Economics Papers from University Paris Dauphine 123456789/13220, Paris Dauphine University.
  3. Barbera, Salvador & Dutta, Bhaskar & Sen, Arunava, 2001. "Strategy-proof Social Choice Correspondences," Journal of Economic Theory, Elsevier, vol. 101(2), pages 374-394, December.
  4. Hans Keiding & Bezalel Peleg, 2006. "Binary effectivity rules," Review of Economic Design, Springer, vol. 10(3), pages 167-181, December.
  5. 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.
  6. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
  7. Eric Maskin, 1998. "Nash Equilibrium and Welfare Optimality," Harvard Institute of Economic Research Working Papers 1829, Harvard - Institute of Economic Research.
  8. Allan Feldman, 1980. "Strongly nonmanipulable multi-valued collective choice rules," Public Choice, Springer, vol. 35(4), pages 503-509, January.
  9. Gibbard, Allan, 1974. "A Pareto-consistent libertarian claim," Journal of Economic Theory, Elsevier, vol. 7(4), pages 388-410, April.
  10. Bezalel Peleg, 1997. "Effectivity functions, game forms, games, and rights," Social Choice and Welfare, Springer, vol. 15(1), pages 67-80.
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  1. repec:hal:cesptp:hal-00666816 is not listed on IDEAS
  2. Agnieszka Rusinowska, 2013. "Bezalel Peleg and Hans Peters: Strategic social choice. Stable representations of constitutions," Social Choice and Welfare, Springer, vol. 40(2), pages 631-634, February.

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