Existence Theorems for Generalized Nash Equilibrium Problems

In a recent paper [7], Dutang provided a thorough study of theorems guaranteeing existence of generalized Nash equilibria and analyze the assumptions on practical parametric feasible sets. Motivated by [7], firstly in this paper, we obtain a generalization (Theorem 1) of an equilibrium theorem for a competitive economy due to Arrow and Debreu [1]. Secondly, we show that our previous generalization (Theorem 2) [14] of a social equilibrium existence theorem of Debreu [6] unifies the previous results due to von Neumann, Nash, Debreu, Park, and Dutang. Our arguments are based on the celebrated Eilenberg-Montgomery fixed point theorem. Finally, we add some historical remarks and the contents of our previous works related to our main results. MSC: 47H09