Some General Properties of Non-Cooperative Games

Abstract

Let there be given two strategy sets Σ₁ and Σ₂, and two payoff functions f₁ and f₂ on Σ₁ × Σ₂. This is the usual setting of two-persons-non-cooperative game theory. We are looking for situations (σ̄₁, σ̄₂) ∈ Σ₁ × Σ₂ which exhibit some kind of stability when each player strives to maximize his own payoff. Such situations will be called “equilibria” or “solutions” of the game, and many different kinds have been discovered since the beginning of game theory.