实向量均衡问题系统解集的本质连通区及其应用

The Essential Components of the Solution Set for Real Vector Equilibrium Problems and its Application

通过构造最佳回应对应,利用Kakutani Fan Glicksberg不动点定理,证明了实向量均衡问题系统解的存在性,并导出了在最佳回应拓扑下其解集本质连通区的存在性;最后,作为特例,得到了Nash均衡问题解集本质连通区的存在性结果。

By constructing best-reply correspondence and using kakutani-Fan-Glicksberg fixed point theorem, this paper establishes the existence of the system of real vector equilibrium problem and deduces the existence of essential components under best-reply correspondence topology. Finally, as a special case, the existence of essential components of the solution set for Nash equilibrium problems is established.