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Nash consistent representation of effectivity functions through lottery models

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  • Peleg, Bezalel
  • Peters, Hans

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. 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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Bibliographic Info

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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Web page: http://www.elsevier.com/locate/inca/622836

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Keywords: Effectivity function Game form Nash consistent representation Lottery model;

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  1. Gibbard, Allan, 1974. "A Pareto-consistent libertarian claim," Journal of Economic Theory, Elsevier, vol. 7(4), pages 388-410, April.
  2. Moulin, H. & Peleg, B., 1982. "Cores of effectivity functions and implementation theory," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 115-145, June.
  3. Hans Keiding & Bezalel Peleg, 2004. "Binary Effectivity Rules," Discussion Paper Series dp378, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  4. Bezalel Peleg, 1997. "Effectivity functions, game forms, games, and rights," Social Choice and Welfare, Springer, vol. 15(1), pages 67-80.
  5. 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.
  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.
  7. Eric Maskin, 1998. "Nash Equilibrium and Welfare Optimality," Harvard Institute of Economic Research Working Papers 1829, Harvard - Institute of Economic Research.
  8. Barbera, Salvador & Dutta, Bhaskar & Sen, Arunava, 2001. "Strategy-proof Social Choice Correspondences," Journal of Economic Theory, Elsevier, vol. 101(2), pages 374-394, December.
  9. Abreu, D. & Sen, A., 1989. "Virtual Implementation In Nash Equilibrium," Working Papers e-90-13, Hoover Institution, Stanford University.
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Cited by:
  1. Agnieszka Rusinowska, 2013. "Book review on "Bezalel Peleg and Hans Peters: Strategic Social Choice. Stable Representations of Constitutions", Studies in choice and welfare, Springer, 2010, 154 pp," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00666816, HAL.

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