不确定条件下n人非合作博弈均衡点集的通有稳定性

Generic stability of equilibrium for n-person non-cooperative games under uncertainty

基于经典博弈模型的Nash均衡点集的通有稳定性和具有不确定参数的n人非合作博弈均衡点的概念,探讨了具有不确定参数博弈的均衡点集的通有稳定性.参照Nash均衡点集稳定性的统一模式,构造了不确定博弈的问题空间和解空间,并证明了问题空间是一个完备度量空间,解映射是上半连续的,且解集是紧集(即usco(upper semicontinuous and compact-valued)映射),得到不确定参数博弈模型的解集通有稳定性的相关结论.

Based on the generic stability of equilibrium for classical game and a concept of equilibrium for the n-person non-cooperative games under uncertainty, the generic stability of equilibrium for games under uncertainty is studied. Thanks to the uniform framework of the model of stability of the Nash equilibrium, the solution space and the question space of games under uncertainty are constructed. The question space is proved to be a complete metric space, the solution mapping is upper semi-continuous, and the solution set is compact （i.e., the solution mapping meets the usco property）. Some conclusions are got about the generic stability of the game model under uncertainty.