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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.

Suggested Citation

  • Bezalel Peleg & Hans Peters, 2005. "Nash Consistent Representation of Effectivity Functions through Lottery Models," Discussion Paper Series dp404, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp404
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    Cited by:

    1. Agnieszka Rusinowska, 2013. "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.
    2. Amit Kothiyal & Vitalie Spinu & Peter P. Wakker, 2014. "Average Utility Maximization: A Preference Foundation," Operations Research, INFORMS, vol. 62(1), pages 207-218, February.
    3. Agnieszka Rusinowska, 2013. "Bezalel Peleg and Hans Peters: Strategic social choice. Stable representations of constitutions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 631-634, February.

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    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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