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Complete Characterization of Acceptable Game Forms by Effectivity Functions

  • Bezalel Peleg

    ()

Acceptable game forms were introduced in Hurwicz and Schmeidler (1978). Dutta (1984) considered effectivity functions of acceptable game forms. This paper unifies and extends the foregoing two papers. We obtain the following characterization of the effectivity functions of acceptable game forms: An effectivity function belongs to some acceptable game form if (i) it belongs to some Nash consistent game forms; and (ii) it satisfies an extra simple condition (our (3.1) or (4.2)). (Nash consistent game forms have already been characterized by their effectivity functions in Peleg et al. (2001).) As a corollary of our characterization we show that every acceptable game form violates minimal liberalism.

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Paper provided by The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem in its series Discussion Paper Series with number dp283.

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Length: 19 pages
Date of creation: Jan 2002
Date of revision:
Publication status: Published as "Representation of effectivity functions by acceptable game forms: A complete characterization" in Social Sciences, 2004, vol. 47, pp. 275-287
Handle: RePEc:huj:dispap:dp283
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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. Hurwicz, Leonid & Schmeidler, David, 1978. "Construction of Outcome Functions Guaranteeing Existence and Pareto Optimality of Nash Equilibria," Econometrica, Econometric Society, vol. 46(6), pages 1447-74, November.
  3. Sen, Amartya Kumar, 1970. "The Impossibility of a Paretian Liberal," Scholarly Articles 3612779, Harvard University Department of Economics.
  4. 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.
  5. Sen, Amartya, 1970. "The Impossibility of a Paretian Liberal," Journal of Political Economy, University of Chicago Press, vol. 78(1), pages 152-57, Jan.-Feb..
  6. Dutta, Bhaskar, 1984. "Effectivity Functions and Acceptable Game Forms," Econometrica, Econometric Society, vol. 52(5), pages 1151-66, September.
  7. Bezalel Peleg, 1997. "Effectivity functions, game forms, games, and rights," Social Choice and Welfare, Springer, vol. 15(1), pages 67-80.
  8. Deb, Rajat & Pattanaik, Prasanta K. & Razzolini, Laura, 1997. "Game Forms, Rights, and the Efficiency of Social Outcomes," Journal of Economic Theory, Elsevier, vol. 72(1), pages 74-95, January.
  9. Hans Keiding & Bezalel Peleg, 1999. "Stable Voting Procedures for Committees in Economic Environments," Discussion Papers 99-20, University of Copenhagen. Department of Economics.
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