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

• Published in: Journal of optimization theory and applications Vol. 135; no. 2; pp. 217 - 239
• Main Authors: NISHIZAKI, I, NOTSU, T
• Format: Journal Article
• Language: English
• Published: New York, NY Springer 01-11-2007; Springer Nature B.V
• Subjects: Applied sciences; Equilibrium; Exact sciences and technology; Game theory; Games; Linear programming; Mathematical models; Mathematical programming; Objectives; Operational research and scientific management; Operational research. Management science; Optimization; Strategy; Studies; Nondominated equilibrium solutions; Non zero sum game; Multiobjective programming; Two person game; Mixed strategy; Multiobjective two-person nonzero-sum games; Equilibrium condition; Mathematical programming problems; Mathematical programming
• ISSN: 0022-3239; 1573-2878
• DOI: 10.1007/s10957-007-9245-6

With reference to a multiobjective two-person nonzero-sum game, we define nondominated equilibrium solutions and provide a necessary and sufficient condition for a pair of mixed strategies to be a nondominated equilibrium solution. Using the necessary and sufficient condition, we formulate a mathematical programming problem yielding nondominated equilibrium solutions. We give a numerical example and demonstrate that nondominated equilibrium solutions can be obtained by solving the formulated mathematical programming problem.