Loeb-measurable solutions to *finite games
\(F=\{1,...,\gamma \}\) 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.
scientific article; zbMATH DE number 3912153
scientific article