The Minmax Theorem for U.S.C.-L.S.C. payoff functions
type: Item
instance of: scholarly article
title: The Minmax Theorem for U.S.C.-L.S.C. payoff functions
zbMATH Open document ID: 0611.90105
DOI: 10.1007/BF01769388
published in: International Journal of Game Theory
publication date: 1986-01-01T00:00:00Z
review text: Our aim is to get a ''general minimax theorem'' whose assumptions and conclusions are phrased only in terms of the data of the problem, i.e. the pair of pure strategy sets S and T and the payoff function on \(S\times T\). For the assumptions, this means that we want to avoid any assumption of the type ''there exists a topology (or a measurable structure) on S and (or) T such that...'' For the conclusions, we are led to require that players have \(\epsilon\)-optimal strategies with finite support, both because those are the easiest to describe in intrinsic terms, and because in any game where the value would not exist in strategies with finite support, all known general minmax theorems implicitly select as ''value'' either the sup inf or the inf sup by in effect restricting either player I or player II arbitrarily to strategies with finite support - so that the resulting ''value'' is completely arbitrary and misleading.
Mathematics Subject Classification ID: 91A05
zbMATH DE Number: 3989135
zbMATH Keywords: general minimax theorem
zbMATH Keywords: \(\epsilon \)-optimal strategies
author: Jean-François Mertens
MaRDI profile type: Publication
cites work: Q5561633
cites work: Contributions to the Theory of Games (AM-39), Volume III
cites work: Advances in Game Theory. (AM-52)
cites work: Q5343895
cites work: Criteres de Compacite dans les Espaces Fonctionnels Generaux
cites work: Sur Les Applications Lineaires Faiblement Compactes D'Espaces Du Type C(K)
cites work: Q5799972
cites work: Q5801635
cites work: Q3226265
cites work: Q5723419
cites work: Q5809478
cites work: On von Neumann's minimax theorem
cites work: Q5632378
cites work: Q3245651
cites work: On general minimax theorems
cites work: Q3245648
cites work: Minimax Theorems on Conditionally Compact Sets
cites work: Generalization of a theorem by v. Neumann concerning zero sum two person games
cites work: Note on zero sum two person games
cites work: Solution for a class of repeated games without a recursive structure
description: scientific article; zbMATH DE number 3989135