Extremality and equilibrium for specified functions and game models. I. Weak equilibria

Notions of extremality with respect to two and more functions are introduced and the concepts of equilibrium points which include, as a particular case, the classical -concepts of equilibrium are defined. The results may be useful in analysis of multiplayer games, static, multi-step, and differential, as is done with the concepts of the saddle point, the Nash equilibrium, the Pareto set, etc.