不确定性下多主从博弈中均衡的存在性

Existence of equilibrium points for multi-leader-follower games under uncertainty

在已知不确定参数变化范围的假设下,研究多主从博弈中均衡点的存在性问题.基于非合作博弈中NS均衡的定义,提出不确定性下多主从博弈中均衡的概念.基于Fan-Glicksberg不动点定理,证明均衡点的存在性.最后通过算例验证了所提出方法的可行性.

Under the assumption that the domain of the undetermined parameters is known,the existence of equilibrium points for multi-leader-follower games under uncertainty is studied.On the basis of NS equilibrium for noncooperative games,equilibrium points for multi-leader-follower games under uncertainty are defined.Further,the existence theorem of equilibrium points for multi-leader-follower games under uncertainty is proved by using Fan-Glicksberg fixed point theorem. Finally,a numeric example illustrates the feasibility of the proposed method.