Online generalised Nash equilibrium seeking over switching communication topologies: a distributed primal–dual approach

This paper investigates distributed online non-cooperative games (NCG) problem with stochastic cost functions over time-varying unbalanced digraphs, where each player aims to minimise the expectation of their own objective functions. It is assumed that the strategy of each player is constrained by its local feasible set and time-varying coupled inequalities, and the local objective function is revealed to it only after each decision. To seek the sequence of generalised Nash equilibria (GNE) in the considered environment, a new distributed online stochastic algorithm leveraging the primal–dual method and push-sum protocol is developed. Under mild conditions, high-probability bounds on the dynamic regret and constraint violation are established, both of which are shown to be sublinear. Finally, the effectiveness of the proposed algorithm is verified via an online electricity market game example.