Strategic games with security and potential level players
AbstractThis paper examines the existence of strategic solutions to finite normal form games under the assumption that strategy choices can be described as choices among lotteries where players have security- and potential level preferences over lotteries (e.g., Cohen, Theory and Decision, 33, 101â€“104, 1992, Gilboa, Journal of Mathematical Psychology, 32, 405â€“420, 1988, Jaffray, Theory and Decision, 24, 169â€“200, 1988). Since security- and potential level preferences require discontinuous utility representations, standard existence results for Nash equilibria in mixed strategies (Nash, Proceedings of the National Academy of Sciences, 36, 48â€“49, 1950a, Non-Cooperative Games, Ph.D. Dissertation, Princeton University Press, 1950b) or for equilibria in beliefs (Crawford, Journal of Economic Theory, 50, 127â€“154, 1990) do not apply. As a key insight this paper proves that non-existence of equilibria in beliefs, and therefore non-existence of Nash equilibria in mixed strategies, is possible in finite games with security- and potential level players. But, as this paper also shows, rationalizable strategies (Bernheim, Econometrica, 52, 1007â€“1028, 1984, Moulin, Mathematical Social Sciences, 7, 83â€“102, 1984, Pearce, Econometrica, 52, 1029â€“1050, 1984) exist for such games. Rationalizability rather than equilibrium in beliefs therefore appears to be a more favorable solution concept for games with security- and potential level players. Copyright Springer Science+Business Media, LLC 2007
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Bibliographic InfoArticle provided by Springer in its journal Theory and Decision.
Volume (Year): 63 (2007)
Issue (Month): 1 (August)
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Web page: http://www.springerlink.com/link.asp?id=100341
Allais paradoxes; equilibrium in beliefs; Nash equilibrium; non-expected utility theories; rationalizability; C72; D81;
Find related papers by JEL classification:
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
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