Extended Nash Equilibria and Their Applications

该基金将资助与扩展纳什均衡的计算和分析有关的研究，这些研究在运筹学中有许多应用，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，建议的工作将侧重于设计快速有效的方法，用于(a)计算具有最多一次可微的成本函数的标准纳什均衡，以及(b)解决广义纳什博弈（即具有联合约束的博弈），多领导-追随者博弈（包括Stackelberg博弈，即具有一个领导者和多个追随者的博弈），寻求连续时间解决轨迹和不平衡路径的动态纳什博弈，具有随机元素的纳什博弈（例如，玩家的优化问题是带有追索权的随机程序），以及玩家串通以增加纳什收益的共谋博弈。我们还将调查网络上一些扩展游戏的无政府状态价格。应用领域提供了丰富的开放问题来源，包括这里提到的所有具有挑战性的特征：联合约束、分层结构、动力学、随机性和共谋。

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.