多目标连续博弈混合弱Pareto-Nash平衡点的存在性

The existence of mixed weakly Pareto-Nash equilibrium points of multi-objective continuous games

首先给出了纯策略集是紧度量空间的多目标连续博弈混合弱Pareto-Nash平衡点的定义,其次证明了此多目标连续博弈的混合弱Pareto-Nash平衡点的存在性.作为应用,我们导出了Glicksberg在1952年所证明的连续博弈混合策略Nash平衡点的存在性.

In this paper, we first give the notion of weakly Pareto-Nash equilibrium points in multiobjective continuous games with compact metric spaces of pure strategies. Then we prove that the existence theorem of weakly Pareto-Nash equilibrium points for multiobjective continuous games. As applications, we show the existence of Nash equilibrium points of continuous games which Glicksberg proved in 1952.