An early paper on the refinement of Nash equilibrium
type: Item
instance of: scholarly article
title: An early paper on the refinement of Nash equilibrium
zbMATH Open document ID: 0944.91004
DOI: 10.1215/S0012-7094-95-08107-1
author: Roger B. Myerson
published in: Duke Mathematical Journal
publication date: 1996-05-21T00:00:00Z
review text: The paper consists of two parts: the text of a student paper that the author wrote in 1974 and a preface in which he explains the historical interest of this document, which was written at a time of transition in game theory. In his 1974 paper, he introduced a refinement of Nash equilibrium which he called ``proper equilibrium''. This concept is similar to Selten's trembling-hand perfect equilibrium but was developed independently of the latter. Later on, he wrote another paper [``Refinements of the Nash equilibrium concept'', Int. J. Game Theory 7, 73-80 (1979; Zbl 0392.90093), in which he used the term ``proper equilibrium'' with a new meaning. The mathematical result of the 1974 paper is the following extension of Kakutani's fixed point theorem: If \(S\) is a non-empty compact convex subset of a finite-dimensional real vector space and \(g\) is an upper-semicontinuous correspondence from \(S\) to (the subsets of) \(S\) with \(g(x)\) nonempty and convex for any \(x\) in the relative interior of \(S\), then \(g\) has a fixed point.
reviewed by: Françoise Forges
Mathematics Subject Classification ID: 91A07
Mathematics Subject Classification ID: 91A10
Mathematics Subject Classification ID: 91B50
zbMATH DE Number: 880071
zbMATH Keywords: proper equilibrium
zbMATH Keywords: Nash equilibrium
zbMATH Keywords: fixed point theorem
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 880071