一类主从博弈Nash均衡点的存在性和稳定性

The Existence and Stability of Nash Equilibrium Points for Single-Leader-Multi-Follower Games

针对单个领导者与多个跟随者的主从博弈,在较弱的条件下,利用Berge极大值定理、Fan-Glicksberg不动点定理,证明了一类主从博弈Nash均衡点的存在性,推广和改进了已有的一些结果.在均衡点的稳定性方面,从最佳回应拓扑的角度证明了此类主从博弈存在Nash均衡点集的本质连通区.

Aiming at the leader-follower game between single leader and multiple followers,the existence of Nash equilibrium point for single-leader-multi-follower games is proved by using the Berge maximum theorem and the Fan-Glicksberg fixed point theorem under the weak condition,and some of the new results have promotion and improvement.In terms of the stability of equilibrium point,it is proved from the viewpoint of best response topology that the single-leader-multi-follower games have the essential components of the Nash equilibrium point sets.