可行策略对应的图像拓扑下广义博弈Nash平衡的稳定性

The stability of Nash equilibria for generalized games under graph topology of feasible strategy correspondence

以往关于广义博弈Nash平衡的稳定性的研究,均利用可行策略映射之间的一致度量.现考虑在更弱的度量下,利用可行策略映射图像之间的Hausdorff距离定义度量.在此弱图像拓扑下,证明了广义博弈空间的完备性,以及Nash平衡映射的上半连续性和紧性,进而得到广义博弈Nash平衡的通有稳定性.即在Baire分类的意义下,大多数的广义博弈都是本质的.

For the stability of generalized games＇ Nash equilibria, current researches are investigated by uniform metric topology of feasible strategy correspondence. However, this paper presents a weaker metric and uses Hausdorff distance of graph of feasible strategy correspondence to study the stability of Nash equilibria. Under weaker graph topology, we prove that the space of generalized games is complete, and Nash equilibrium correspondence is upper semi-continuous and compact-valued. These lead to generic stability of generalized games＇ Nash equilibria, i.e., in the sense of Baire category, most of generalized games are essential.