Egalitarian solutions of large games. 1. A continuum of players

This is the first of two papers devoted to the study of egalitarian solutions for nontransferable utility games with a large number of players. This paper is concerned with the construction of egalitarian solutions for the limit Situation with a continuum of players. We build on the concept of the Potential introduced in Hart and MasColell and exploit partial differential equations techniques. In particular, we associate to the egalitarian solutions a variational problem which may be viewed as a generalization – to the nontransferable utility context – of the diagonal principle of Aumann and Shapley in the transferable utility setting.