Extended Nash Equilibria and Their Applications

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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.