Nash equilibria of generalized games in normed spaces without upper semicontinuity

The aim of this paper is to prove an existence theorem for the Nash equilibria of a noncooperative generalized game with infinite-dimensional strategy spaces. The main peculiarity of this result is the absence of upper semicontinuity assumptions on the constraint multifunctions. Our result is in the same spirit of the paper Cubiotti (J Game Theory 26: 267–273, 1997), where only the case of finite-dimensional strategy spaces was considered.