Minimax selection theorems
type: Item
instance of: scholarly article
title: Minimax selection theorems
zbMATH Open document ID: 0589.90088
DOI: 10.1016/0022-247X(84)90161-6
published in: Journal of Mathematical Analysis and Applications
publication date: 1984-01-01T00:00:00Z
review text: Consider a two-person zero-sum game G modelled as follows: \(G=(S,{\mathcal S},X,Y,C,r)\), where (S,\({\mathcal S})\) is a measurable state space, X and Y are action spaces for two players, \(C=\{(s,x,y):\) \(s\in S\), (s,x)\(\in A\) and (s,y)\(\in B\}\), where \(A\subset S\times X\), \(B\subset S\times Y\), and \(r: C\to R\) is the payoff function. The paper gives three different sets of sufficient assumptions on the primitive data of G for the measurability of the (lower) value, which is a function of the state variable, as well as for the existence, for either or both players, of measurable optimal or \(\epsilon\)-optimal strategies.
Mathematics Subject Classification ID: 91A05
Mathematics Subject Classification ID: 91A20
Mathematics Subject Classification ID: 91A60
Mathematics Subject Classification ID: 28A05
zbMATH DE Number: 3948029
zbMATH Keywords: minimax selection theorems
zbMATH Keywords: two-person zero-sum game
zbMATH Keywords: measurable state space
zbMATH Keywords: measurability of the (lower) value
zbMATH Keywords: existence
zbMATH Keywords: measurable optimal or \(\epsilon \) -optimal strategies
author: Andrzej S. Nowak
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3948029