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Nash Consistent Representation of Effectivity Functions through Lottery Models

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Author Info
Bezalel Peleg ()
Hans Peters ()

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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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Paper provided by Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp404.

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

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  1. Barbera, Salvador & Dutta, Bhaskar & Sen, Arunava, 2001. "Strategy-proof Social Choice Correspondences," Journal of Economic Theory, Elsevier, vol. 101(2), pages 374-394, December. [Downloadable!] (restricted)
  2. Gibbard, Allan, 1974. "A Pareto-consistent libertarian claim," Journal of Economic Theory, Elsevier, vol. 7(4), pages 388-410, April. [Downloadable!] (restricted)
  3. Moulin, H. & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 115-145, June. [Downloadable!] (restricted)
  4. Hans Keiding & Bezalel Peleg, 2004. "Binary Effectivity Rules," Discussion Paper Series dp378, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem. [Downloadable!]
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  5. Bezalel Peleg, 1997. "Effectivity functions, game forms, games, and rights," Social Choice and Welfare, Springer, vol. 15(1), pages 67-80. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
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  1. Joseph Abdou, 2009. "The Structure of Unstable Power Systems," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00389181_v1, HAL. [Downloadable!]
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