The core of a class of non-atomic games which arise in economic applications
The authors study cooperative games \(v\) with infinite many players \(T\) and a \(\sigma\)-field \(\Sigma\) of coalitions. It is assumed that the characteristic function \(v\) is a non-atomic measure which fulfills some continuity conditions with respect to the appropriate topology of the set of bounded countably additive non-atomic measures on \((T,\Sigma)\). The main results concern the non-emptiness of the core in the case of concavity of the continuous extension \(\bar{v}\). Moreover representation theorems for the core are given. The results are illustrated by well-known market game examples from the literature.
scientific article; zbMATH DE number 1309798