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 contex we consider vNM-Stable Sets according to von Neumann and Morgenstern. It is shown that we can classify or characterize all solutions of this type which are convex polyhedra, i.e., which are the convex hull of finitely many measures. We also compare this with the case of a finite game. For certain classes of glove games we optain a characterization also in the finite case using the results from the continuum.