Remarks on Nash equilibria for games with additively coupled payoffs

Summary 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.I wish to thank Nicholas Yannelis for posing a question which led me to writing this note in its present form.