随机广义纳什均衡问题的研究及应用

项目名称： 随机广义纳什均衡问题的研究及应用

项目编号： No.11501476

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 李沛瑜

作者单位： 西南石油大学

项目金额： 18万元

中文摘要： 广义纳什均衡问题（GNEP）是每一个参与者的决策集合受制于其他参与者的决策的纳什均衡问题，众多的科研工作者对GNEP从理论、算法、应用模型等方面进行了广泛深入的研究。然而求解出所有的GNEP均衡解是很困难的，因此我们更多的是关注一些具有现实应用背景的特殊GNEP模型，研究其一些特殊的均衡解和稳定点，如价值函数具有权重参数可分离或完全可分离结构且包含共用约束GNEP模型的正则均衡解和正则稳定点。由于很多实际问题会涉及随机因素，研究含有随机因素的GNEP（SGNEP）也非常具有现实意义。本项目拟考虑将这些价值函数具有特殊结构且有现实应用背景的SGNEP，利用样本均值逼近方法（SAA）把SGNEP转化为确定性的GNEP，根据其特殊性进而提出一些有效的求解方法。特别地，针对更难求解的具有共用均衡约束的SGNEP，我们考虑求解其稳定点，转化为求解标准的随机均衡约束数学规划问题的稳定点进行研究。

中文关键词： 广义纳什均衡；随机广义纳什均衡；均衡约束；随机规划；稳定点

英文摘要： Generalized Nash equilibrium problem (GNEP) is a Nash equilibrium problem, in which each player's strategy set may depend on the rivals' strategies and it has been extensively studied about the existence theory, numerical algorithms, and applications of GNEP. Since it is difficult to find all equilibrium points or as many equilibrium points as possible, an alternative approach is to single out a equilibrium point that has some special property. We studies a class of generalized Nash equilibrium problems which is separable with positive weights or completely separable, and solve its normalized equilibrium points and normalized stationary points. On the other hand, since some elements may involve uncertain data in many practical problems, the stochastic generalized Nash equilibrium problems (SGNEP) have been drawing attentions in the recent. The aim of this project is to apply the well-known sample average approximation (SAA) method reformulating SGNEP to GNEP, and single out a equilibrium point that has some special property. Specially, for more difficult to solve SGNEP with equilibrium constraints, we consider solving its stationary point, and reformulate it to a standard stochastic mathematical programs with equilibrium constraints.

英文关键词： Generalized Nash equilibrium;Stochastic generalized Nashequilibrium;Equilibrium constraint;Stochastic programming;Stationary points