Distributed Generalized Nash Equilibrium Seeking for Purely Monotone Games Under Communication Constraints

This paper investigates the distributed generalized Nash equilibrium (GNE) seeking problem for purely monotone games with set and shared affine inequality constraints over communication-constrained networks. A continuous-time projected dynamical system is developed by combining a regularization technique with a penalty method, which converts the original purely monotone constrained game into a strongly monotone surrogate problem. To alleviate the network communication burden, an event- and switching-activated localized communication mechanism is formulated, where agents transmit information only when local estimation errors exceed dynamic threshold or when topology switching occurs. By properly designing the dynamic triggering threshold and the time-varying parameters, the communication-induced errors are suppressed, and the proposed algorithm is shown to converge asymptotically to the least-norm variational GNE without Zeno behavior. Finally, illustrative simulations are conducted to demonstrate the viability and efficiency of the developed strategy.