On the existence of strategic solutions for games with security- and potential level players

Zimper, Alexander

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URL: http://ub-madoc.bib.uni-mannheim.de/2740
URN: urn:nbn:de:bsz:180-madoc-27402
Document Type: Working paper
Year of publication: 2004
The title of a journal, publication series: None
Publication language: English
Institution: School of Law and Economics > Sonstige - Fakultät für Rechtswissenschaft und Volkswirtschaftslehre
MADOC publication series: Sonderforschungsbereich 504 > Rationalitätskonzepte, Entscheidungsverhalten und ökonomische Modellierung (Laufzeit 1997 - 2008)
Subject: 330 Economics
Classification: JEL: C72 D81 ,
Subject headings (SWD): Risikoverhalten , Nichtkooperatives Spiel , Entscheidung bei Unsicherheit
Keywords (English): Non-expected utility theories , Allais paradoxa , equilibrium in beliefs , Nash equilibrium , trembling hand perfect equilibrium , rationalizability
Abstract: This paper examines the existence of strategic solutions for 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., Gilboa, 1988; Jaffray, 1988; Cohen, 1992). Since security- and potential level preferences require discontinuous utility representations, standard existence results for Nash equilibria in mixed strategies (Nash, 1950a,b) or for equilibria in beliefs (Crawford, 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, 1984; Moulin, 1984; Pearce, 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.
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