Egalitarian Solutions of Large Games: I. A Continuum of Players

This is the first of two papers devoted to the study of egalitarian solutions for nontransferable utility (NTU) 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 Mas-Colell (Hart, S., A. Mas-Colell. 1989. Potential, value and consistency. Econometrica57 589–614.) 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 (Aumann, R. J., L. S. Shapley. 1974. Values of Non-Atomic Games. Princeton University Press, Princeton, New Jersey.) in the transferable utility setting.