Loeb-measurable solutions to *finite games
type: Item
instance of: scholarly article
title: Loeb-measurable solutions to *finite games
zbMATH Open document ID: 0571.90108
DOI: 10.1016/0165-4896(85)90058-7
author: Alain A. Lewis
published in: Mathematical Social Sciences
publication date: 1985-01-01T00:00:00Z
review text: \(F=\{1,...,\gamma \}\) is an internal *finite subset of \(^*N\), where \(\gamma\) is an infinite integer. A *finite cooperative game is \(\Gamma_ F(^*v)=<F,{\mathcal A}(F),^*v>\). Here F is the space of players, \({\mathcal A}(F)\) is the internal algebra of the internal subsets of F (interpreted as the coalition space), \(^*v\) is a nonnegative function defined on \({\mathcal A}(F)\) with values in \(^*R\) (interpreted as the characteristic function). It is assumed that (i) \(^*v(\emptyset)=0\), (ii) \(^*v(\{j\})=0\), (iii) \(^*v(S\cup T)\gtrsim^*v(S)+^*v(T)\) for S, \(T\in {\mathcal A}(F)\) and \(S\cap T=\emptyset\), (iv) \(0<^*v(F)<\eta\) for some \(\eta \in^*N\). It is shown that the space of S-imputations of a game contains two nonempty subsets, namely the quasi-kernel and the S- bargaining set. Both are external solution concepts.
Mathematics Subject Classification ID: 91A07
Mathematics Subject Classification ID: 03H10
Mathematics Subject Classification ID: 91A12
Mathematics Subject Classification ID: 91A40
zbMATH DE Number: 3912153
zbMATH Keywords: von Neumann games
zbMATH Keywords: nonstandard analysis
zbMATH Keywords: solution concepts
zbMATH Keywords: Loeb spaces
zbMATH Keywords: star-finite cooperative game
zbMATH Keywords: quasi-kernel
zbMATH Keywords: S-bargaining set
MaRDI profile type: Publication
full work available at URL: 0165-4896(85)90058-7
OpenAlex ID: W2082734726
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description: scientific article; zbMATH DE number 3912153