Mathematical Sciences: Algorithms and Existence Theorems for Cooperative and Stochastic Games

本项目将研究博弈论中的一系列问题：a)任意状态空间中单控制器和切换控制器博弈是否存在纳什均衡？b)对于未折现的博弈，ARAT博弈和切换控制博弈是否承认平稳纳什均衡？c)通过适当定义Sobolev简化子对策来表征多选择核仁；d)找到一种有效的算法来求解流对策、线性约束对策和齐次对策的核心。博弈论的方法、技术和思想在经济学、运筹学、排队论和控制论中都有应用。

This project will study a diverse set of questions in games theory: a) Do Nash equilibria exist for single controller and switching controller games in arbitrary state spaces? b) Do ARAT games and switching control games admit stationary Nash equilibrium for undiscounted games? c) Characterize multi-choice nucleolus by suitably defining Sobolev's reduced subgames; d) Find an efficient algorithm to solve for the nucleolus of flow games, linearly constrained games, and homogeneous games. %%% Methods, techniques and ideas of games theory have applications to economics, operations research, queuing theory, and control theory.