Network Games Equilibrium Computation: Duality Extension and Coordination
Résumé
We formulate a generic network game as a generalized Nash equilibrium problem. Relying on normalized Nash equilibrium as solution concept, we provide a parametrized proximal algorithm to span many equilibrium points [1]. Complexifying the setting, we consider an information structure in which the agents in the network can withhold some local information from sensitive data, resulting in private coupling constraints. The convergence of the algorithm and deviations in the players’ strategies at equilibrium are formally analyzed. In addition, duality theory extension enables to use the algorithm to coordinate the agents through a fully distributed pricing mechanism, on one specific equilibrium with desirable properties at the system level (economic efficiency, fairness, etc.). To that purpose, the game is recast as a hierarchical decomposition problem in the same spirit as in [3], and a procedure is detailed to compute the equilibrium that minimizes a secondary cost function capturing system level properties. Finally, applications are presented to a) peer-to-peer energy trading [2], b) Transmission-Distribution System Operators markets for flexibility procurement [4].