有限理性下参数最优化问题解的稳定性

主要研究有限理性下参数最优化问题解的稳定性. 即在两类扰动即目标函数及可行集二者, 目标函数、可行集及参数三者分别同时发生扰动的情形下, 对参数最优化问题引入一个抽象的理性函数, 分别建立了参数最优化问题的有限理性模型M, 运用``通有'的方法, 得到了上述两种扰动情形下相应的有限理性模型M的结构稳定性及对\varepsilon-平衡(解)的鲁棒性, 即有限理性下绝大多数的参数最优化问题的解都 是稳定的, 并以一个例子说明所得的稳定性结果均是正确的.

Stability of solutions to parametric optimization problems under bounded rationality

Parametric optimization has been widely applied in game theory, control theory,economics and management, engineering technology, etc. Recently, the stabilityof solutions to parametric optimization has attracted increasing attention.This paper mainly studies the stability of solutions to parametric optimizationproblems under bounded rationality. By introducing an abstract rationality function,two rational models M are established with two types of perturbations: theperturbation of both objective functions and feasible sets, and the perturbation ofobjective functions, feasible sets and parameters simultaneously. For the twoperturbations above, by the ``generic' method, the rational model M is structurallystable and is robust to \varepsilon-equilibria (or solutions), respectively.That is, the solutions to most of parametric optimization problems are stablein the sense of Baire category. Finally, an example is illustrated.