Pareto Optimality and Equilibria in Noncooperative Games

Abstract

This chapter considers the Nash equilibrium strategy profiles that are Pareto optimal with respect to the rest of the Nash equilibrium strategy profiles. The sufficient conditions for the existence of such pure strategy profiles are established. These conditions employ the Germeier convolutions of the payoff functions. For the noncooperative games with compact strategy sets and continuous payoff functions, the existence of the Pareto-optimal Nash equilibria (PoNE) in mixed strategies is proven.

On the Concept of Equilibrium in Sanctions and Countersanctions in a Differential Game

“…finally yields (17). Thus, a Pareto-maximal alternative U P in the multicriteria choice problem Γ v is given by ( 17) and ( 18).…”

“…Various concepts of static [12] and active equilibria [13] are adopted to balance controlled systems [14,15] in game-theoretic economic-mathematical modeling. If an analytically constructed differential game describes decision-making in a complex system, then, according to leading researchers, equilibrium as an acceptable solution of a differential game should have the property of stability [16][17][18]. In a practical interpretation, stability means no player will increase their payoff by any unilateral deviation from equilibrium.…”