Nondominated equilibrium solutions of a multiobjective two-person nonzero-sum game and the corresponding mathematical programming problem

Abstract

In this paper, we deal with multiobjective two-person non-zero-sum games, and define nondominated equilibrium solutions of the games as an extension of the concept of Pareto equilibrium solutions. To obtain the nondominated equilibrium solutions, we formulate mathematical programming problems whose decision variables correspond to mixed strategies of players, and show that optimal solutions to the formulated problems are nondominated equilibrium soultions.