Asymptotic Value of Mixed Games

Abstract

In this paper we are concerned with mixed games, i.e., games with on one hand an “ocean” of insignificant players (formalized by a continuum of players) and on the other hand some significant players (atoms). Considering these games as limits of finite games, we show, for the subset pFL, that the Shapley-Hart value of the mixed game corresponding to the uniform probability measure is the limit of the Shapley values of the associated finite games. This paper should then be considered as a generalization of the results of the work by Aumann-Shapley on nonatomic games.