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Nash consistent representation of effectivity functions through lottery models

  • Peleg, Bezalel
  • Peters, Hans

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. The latter means that there exists a finite game form which represents the lottery model and which has a Nash equilibrium for any profile of utility functions satisfying the minimal requirement of respecting first order stochastic dominance among lotteries. No additional condition on the original effectivity function is needed.

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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 65 (2009)
Issue (Month): 2 (March)
Pages: 503-515

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Handle: RePEc:eee:gamebe:v:65:y:2009:i:2:p:503-515
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  1. Moulin, Hervé & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Economics Papers from University Paris Dauphine 123456789/13220, Paris Dauphine University.
  2. 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.
  3. Bezalel Peleg, 1997. "Effectivity functions, game forms, games, and rights," Social Choice and Welfare, Springer, vol. 15(1), pages 67-80.
  4. Barbera, Salvador & Dutta, Bhaskar & Sen, Arunava, 2001. "Strategy-proof Social Choice Correspondences," Journal of Economic Theory, Elsevier, vol. 101(2), pages 374-394, December.
  5. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
  6. 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.
  7. Allan Feldman, 1980. "Strongly nonmanipulable multi-valued collective choice rules," Public Choice, Springer, vol. 35(4), pages 503-509, January.
  8. Eric Maskin, 1998. "Nash Equilibrium and Welfare Optimality," Harvard Institute of Economic Research Working Papers 1829, Harvard - Institute of Economic Research.
  9. Gibbard, Allan, 1974. "A Pareto-consistent libertarian claim," Journal of Economic Theory, Elsevier, vol. 7(4), pages 388-410, April.
  10. Hans Keiding & Bezalel Peleg, 2004. "Binary Effectivity Rules," Discussion Paper Series dp378, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
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