Browder type fixed point theorems and Nash equilibria in generalized games

In this paper, we present two generalizations of the well-known Browder fixed point theorem, one of which is equivalent to the well-known Fan-Knaster-Kuratowski-Mazurkiewicz theorem. As applications, we apply these fixed point theorems to derive existence theorems for Nash equilibria in generalized games which generalize some existing existence theorems in the literature, including the well-known equilibrium existence theorem by Arrow and Debreu (Econometrica 22:265-290, 1954) and the existence theorem by Cubiotti (Int J Game Theory 26:267-273, 1997).