On the existence of equilibria in generalized games

This paper deals with the existence of equilibrium in generalized games (the so-called abstract economies) and Nash equilibrium in games with general assumptions. Preference correspondences, unlike the existing theorems in the literature, need not have open graphs or open lower sections, strategy spaces need not be compact and finite dimensional, the number of agents need not be countable, and preference relations need not be ordered. Thus, our results generalize many of the existence theorems on equilibria in generalized games, including those of Debreu (1952), Shafer and Sonnenschein (1975), Toussaint (1984), Kim and Richter (1986), and Yannelis (1987).I wish to thank the editor and an anonymous referee for helpful comments and suggestions.