论文标题
通用纳什游戏和准优化问题的最佳近似解决方案
Best Approximate Solution for Generalized Nash Games and Quasi-optimization Problems
论文作者
论文摘要
在本文中，我们考虑了广义的NASH游戏，其中关联的约束图不一定是自我。对于此类游戏，经典的NASH平衡可能不存在，因此我们介绍了此类游戏的最佳近似解决方案的概念。我们研究了这种通用的NASH游戏的最佳近似解决方案的发生，该游戏由无限的许多玩家组成，其中每个玩家都调节位于拓扑矢量空间中的策略变量。根据Kakutani可分解图的最大定理和固定点结果，我们得出了在准分子coavity和玩家目标函数上的准杂种和弱连续性假设下的最佳近似解决方案的存在。此外，我们证明了出现准优化问题的最佳近似解决方案。
In this article, we consider generalized Nash games where the associated constraint map is not necessarily self. The classical Nash equilibrium may not exist for such games and therefore we introduce the notion of best approximate solution for such games. We investigate the occurrence of best approximate solutions for such generalized Nash games consisting of infinitely many players in which each player regulates the strategy variable lying in a topological vector space. Based on the maximum theorem and a fixed point result for Kakutani factorizable maps, we derive the existence of best approximate solutions under the quasi-concavity and weak continuity assumption on players' objective functions. Furthermore, we demonstrate the occurrence of best approximate solutions for quasi-optimization problems.
