Distributed generalized Nash equilibrium seeking: event-triggered coding-decoding-based secure communication

In this paper, we consider the distributed generalized Nash equilibrium (GNE) seeking problem in strongly monotone games. The transmission among players is implemented through a digital communication network with limited bandwidth. For improving communication efficiency or/and security, an event-triggered coding-decoding-based communication is first proposed, where the data (decision variable) are first mapped to a series of finite-level codewords and, only when an event condition is satisfied, then sent to the neighboring agents. Moreover, a distributed communication-efficient GNE seeking algorithm is constructed accordingly, and the overrelaxation scheme is further taken into consideration. Through primal-dual analysis, the proposed algorithm is proven to converge to a variational GNE with fixed step-sizes by recasting it as an inexact forward-backward iteration. Finally, numerical simulations illustrate the benefit of the proposed algorithms in terms of saving communication resources.