Stochastic Aggregative Games with Coupled Inequality Constraints

In this paper, stochastic aggregative games are studied, where a group of players aim to selfishly minimize their own expectation-valued cost function relying on its individual strategy and the aggregate of all players’ strategies, simultaneously satisfying shared coupled constraints and local feasible set constraints. To learn the generalized Nash equilibria, a novel distributed stochastic primal-dual push-sum algorithm is designed, which is suitable for time-varying unbalanced iteraction networks. It is rigorously shown that the generated sequence by the devised algorithm converges to its variational generalized Nash equilibrium almost surely. Additionally, the convergence rate of the time-averaged strategy sequence in high probability is derived on the basis of the sub-Gaussian noise model. Finally, the obtained theoretical results are corroborated by numerical simulations.