有限理性与图像拓扑下广义博弈解的稳定性

Bounded Rationality and Stability of Solutions for Generalized Games under Graph Topology

【目的】集值映射的图像拓扑较一致度量产生的拓扑弱,图像拓扑下研究解的稳定性具有重要的理论意义。【方法】有限理性框架下,首先利用可行策略映射图像之间的Hausdorff距离定义度量,其次分别定义可行映射,行为映射和理性函数。【结果】得到了参数空间的完备性和有限理性框架下广义博弈解的通有稳定性。【结论】也就是说,在此弱图像拓扑下证明了大多数的广义博弈(Baire分类的意义下)都是结构稳定的,对ε-平衡也是鲁棒的。

[Purposes]The graph topology of set-valued mappings is weaker than the topology produced by uniform metric;it is of great theoretical significance to study the stability of solutions under graph topology.[Methods]A metric is defined by using the Hausdorff distance of graphs of feasible strategy mappings under the framework of bounded rationality,and concepts of feasible mapping,behavior mapping and rational function are defined respectively.[Findings]Then the completeness of parameter space and the generic stability of solutions for generalized games under bounded rationality are obtained.[Conclusions]Under this weak graph topology,it is proven that the most of generalized games（in the sense of Baire）are structurally stable and robust toε-equilibrium.