Remarks on Nash equilibria for games with additively coupled payoffs (revision, previous title: An unusual Nash equilibrium result and its application to games with allocations in infinite dimensions)

Abstract

If the payoffs of a game are affine, then they are additively coupled. In this situation both the Weierstrass theorem and the Bauer maximum principle can be used to produce existence results for a Nash equilibrium, since each player is faced with an individual, independent optimization problem. We consider two instances in the literature where these simple observations immediately lead to substantial generalizations.