Network Games Equilibrium Computation: Duality Extension and Privacy

We formulate a generic network game as a generalized Nash equilibrium problem. Relying on normalized Nash equilibrium as a solution concept, we provide a parametrized proximal algorithm to span many equilibrium points. 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 of 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, and a procedure is detailed to compute the equilibrium that minimizes a secondary cost function capturing system-level properties. An application is presented to a peer-to-peer energy trading problem, under complete and incomplete information. Under incomplete information, assuming that the agents anticipate the form of the market equilibrium, an aggregative noncooperative stochastic game is formulated to model the communication mechanism between the agents on top of the peer-to-peer energy trading game. Analytical and numerical analyses are provided to capture the impact of privacy constraints on the generalized Nash equilibria.