Uniqueness conditions for point-rationalizable solutions of games with metrizable strategy sets

Zimper, Alexander

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URL: http://ub-madoc.bib.uni-mannheim.de/2757
URN: urn:nbn:de:bsz:180-madoc-27579
Document Type: Working paper
Year of publication: 2003
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 C62 ,
Subject headings (SWD): Nash-Gleichgewicht , Spieltheorie , Nichtkooperatives Spiel
Keywords (English): Uniqueness , existence, point-rationalizability , Nash equilibrium , fixed point theorem , Cournot competition
Abstract: The unique point-rationalizable solution of a game is the unique Nash equilibrium. However, this solution has the additional advantage that it can be justified by the epistemic assumption that it is Common Knowledge of the players that only best responses are chosen. Thus, games with a unique point-rationalizable solution allow for a plausible explanation of equilibrium play in one-shot strategic situations, and it is therefore desireable to identify such games. In order to derive sufficient and necessary conditions for unique point-rationalizable solutions this paper adopts and generalizes the contraction-property approach of Moulin (1984) and of Bernheim (1984). Uniqueness results obtained in this paper are derived under fairly general assumptions such as games with arbitrary metrizable strategy sets and are especially useful for complete and bounded, for compact, as well as for finite strategy sets. As a mathematical side result existence of a unique fixed point is proved under conditions that generalize a fixed point theorem due to Edelstein (1962).
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