Semi-Decentralized Nash Equilibrium Seeking in Aggregative Games With Separable Coupling Constraints and Non-Differentiable Cost Functions

We study the Nash equilibrium seeking problem for noncooperative agents whose decision making process can be modeled as a generalized aggregative game. Specifically, we consider players with convex local cost functions, convex local constraints, and convex separable coupling constraints, and we extend the literature on generalized aggregative games by handling possibly non-differentiable cost functions. We recast the Nash equilibrium seeking problem as the problem to find a zero of a set-valued monotone operator and show that the variational Nash equilibria correspond to KKT solutions of the original game where the shared constraints have the same Lagrange multipliers for all the players. Finally, we design a semi-decentralized algorithm with global convergence guarantee for generalized Nash equilibrium seeking.

I. Introduction

Aggregative games [1] have been recently considered for modeling the decision making process of a population of noncooperative agents, where the decision of each agent is affected by some aggregate effect of all the agents. Application domains with the aggregative feature include the demand side management in the smart grid [2], e.g., for plug-in electric vehicles [3] and thermostatically controlled loads [4], demand response in competitive markets [5] and network congestion control [6].