A characterization of vNM-stable sets for linear production games

Abstract

We discuss linear production games or market games with a continuum of players which are represented as minima of finitely many nonatomic measures.¶Within this context we consider vNM-Stable Sets according to von Neumann and Morgenstern. We classify or characterize all solutions of this type which are convex polyhedra, i.e., which are the convex hull of finitely many imputations. Specifically, in each convex polyhedral vNM-Stable Set (and not only in the symmetric ones), the different types of traders must organize themselves into cartels. The vNM-Stable Set is then the convex hull of the utility distributions of the cartels.¶Using the results from the continuum, we obtain a similar characterization also for finite glove market games.