多目标大博弈中弱Pareto-Berge均衡的存在性

THE EXISTENCE OF WEAKLY PARETO-BERGE EQUILIBRIUM POINTS IN MULTIOBJECTIVE LARGE GAMES

研究了具有任意多个局中人的非合作多目标博弈(多目标大博弈).基于一般非合作博弈中的Berge均衡概念,定义多目标大博弈中的弱Pareto-Berge均衡.进一步推广了截口定理,得到新的截口定理,并且利用这个新的截口定理证明多目标大博弈中弱Pareto-Berge均衡的存在性.多目标大博弈中弱Pareto-Nash均衡的存在性结论可作为弱Pareto-Berge均衡存在性的特例给出.

This paper considers noncooperative multi-objective games with multi-players （multi-objective large game）. According to Berge equilibrium in normal games, we introduce the notion of weakly Pareto-Berge equilibrium in multi-objective large games. By generalizing section theorem, we show the existence of weakly Pareto-Berge equilibrium in multi-objective large games. As a special case, we obtain the existence of weakly Pareto-Nash equilibrium points in multi-objective large games.