Nash Consistent Representation of Effectivity Functions through Lottery Models
AbstractEffectivity 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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Bibliographic InfoPaper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp404.
Length: 16 pages
Date of creation: Sep 2005
Date of revision:
Publication status: Forthcoming in Games and Economic Behavior.
Other versions of this item:
- Peleg, Bezalel & Peters, Hans, 2009. "Nash consistent representation of effectivity functions through lottery models," Games and Economic Behavior, Elsevier, vol. 65(2), pages 503-515, March.
- Peleg,Bezalel & Peters,Hans, 2005. "Nash consistent representation of effectivity functions through lottery models," Research Memorandum 030, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-12-01 (All new papers)
- NEP-GTH-2005-12-05 (Game Theory)
- NEP-HEA-2005-12-15 (Health Economics)
- NEP-UPT-2005-12-01 (Utility Models & Prospect Theory)
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