论文标题
关于求解多项式的广义纳什均衡问题的多面体同位验证方法
On the polyhedral homotopy method for solving generalized Nash equilibrium problems of polynomials
论文作者
论文摘要
广义的NASH平衡问题（GNEP）是一种为一组玩家找到策略的游戏，以便优化每个玩家的目标功能。 GNEP的解决方案称为广义纳什均衡（GNES）。在本文中，我们提出了一种基于多面体同型延续和半衰落弛豫的矩层层次结构的多项式GNEP的数值方法。我们表明，如果存在，我们的方法可以在某些通用假设下找到所有GNE，或者检测GNE的不存在。进行了一些数值实验来证明我们方法的效率。
The generalized Nash equilibrium problem (GNEP) is a kind of game to find strategies for a group of players such that each player's objective function is optimized. Solutions for GNEPs are called generalized Nash equilibria (GNEs). In this paper, we propose a numerical method for finding GNEs of GNEPs of polynomials based on the polyhedral homotopy continuation and the Moment-SOS hierarchy of semidefinite relaxations. We show that our method can find all GNEs if they exist, or detect the nonexistence of GNEs, under some genericity assumptions. Some numerical experiments are made to demonstrate the efficiency of our method.
