An early paper on the refinement of Nash equilibrium
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.
scientific article; zbMATH DE number 880071
scientific article