 Uniqueness conditions for point-rationalizable solutions of games with metrizable strategy setsNo 03-28, Papers from Sonderforschungsbreich 504 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). Keywords: Uniqueness; existence; point-rationalizability; Nash equilibrium; fixed point theorem; Cournot competition (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:mnh:spaper:2757 Access Statistics for this paper More papers in Papers from Sonderforschungsbreich 504 Contact information at EDIRC. |
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