Distributed Online Algorithm with Inertia for Seeking Generalized Nash Equilibria

This paper is concerned with the generalized Nash equilibrium (GNE) seeking problem of noncooperative games in dynamic environments, where the cost function and coupled constraint of each agent are time-varying. In this case, each agent is required to make a decision before obtaining its cost function and a local inequality constraint. The purpose of the addressed problem is to establish a new distributed primary-dual and mirror descent online algorithm with inertia that is capable of seeking the GNE via time-varying communication graphs and has the potential of achieving a low average regret. Then, two information transmission modes and two estimate update strategies are discussed, respectively. Finally, a simulation example is presented to illustrate the effectiveness of the algorithms, and to further compare their performances.