On Noncooperative Games, Minimax Theorems, and Equilibrium Problems

A Discrete Characterization of the Solvability of Equilibrium Problems and Its Application to Game Theory

“…Muu and W. Oettli in [2]. Most results guaranteeing the existence of equilibrium for a scalar function assume topological hypotheses on one variable, and in addition, either convexity or concavity conditions on the other or concavity-convexity assumptions on both variables [3][4][5][6][7][8][9][10]. This kind of problem comprises the study of the celebrated Nash equilibrium [11][12][13][14] and the existence of saddle points or, more generally, the validity of the minimax inequality [15][16][17][18][19][20][21], to name only a few.…”