Extended Nash Equilibria and Their Applications

该补助金为有关计算和分析扩展纳什均衡的研究提供资金，这些纳什均衡来自运筹学中的许多应用，包括电力市场的定价和设计，互联网网络分析，通信系统中的资源分配，不确定环境中的竞争能力扩张，供应链管理以及具有状态动态和控制约束的开环微分博弈。具体来说，所提出的工作将集中在设计快速有效的方法，用于（a）计算标准纳什均衡，成本函数最多只能有一次可微，（B）求解广义纳什博弈（即，具有联合约束的游戏），多领导者-跟随者游戏（其包括Stackelberg游戏，即，具有一个领导者和多个追随者的那些），寻求不均衡的连续时间解轨迹和路径的动态纳什博弈，具有随机元素的纳什博弈（例如，参与人的最优化问题是有追索权的随机规划），以及参与人合谋增加纳什收益的合谋博弈。 我们还将调查网络上一些扩展游戏的无政府状态的价格。 应用领域提供了一个开放的问题，包括这里提到的所有具有挑战性的功能丰富的来源：联合约束，层次结构，动力学，随机和勾结。

This grant provides funding for research pertaining to the computation and analysis of extended Nash equilibria that arise from many applications in operations research, including pricing and design in electric power markets, internet network analysis, resource allocation in communication systems, competitive capacity expansion in uncertain environments, supply chain management, as well as open-loop differential games with state dynamics and control constraints. Specifically, the proposed work will focus on the design of fast efficient methods for (a) computing standard Nash equilibria with cost functions that are at best once differentiable, and (b) solving generalized Nash games (i.e., games with joint constraints), multi-leader-follower games (which include Stackelberg games, i.e., those with one leader and multiple followers), dynamic Nash games for which continuous-time solution trajectories and pathways of disequilibria are sought, Nash games with random elements (e.g., players' optimization problems are stochastic programs with recourse), as well as collusive games where players collude toincrease their Nash payoffs. We will also investigate the price of anarchy for some extended games on networks. The application areas provide a rich source of open problems that encompass all the challenging features mentioned here: joint constraints, hierarchical structure, dynamics, stochastics, and collusion.