Distributed Nash Equilibrium Seeking for Constrained Aggregative Games over Jointly Connected and Weight-Balanced Switching Networks
Zhaocong Liu, Jie Huang
TL;DR
The paper addresses constrained distributed Nash equilibrium seeking for aggregative games on a jointly connected and weight-balanced switching network $\\mathcal{G}_{\\rho(t)}$, where network Topology may be directed and intermittently disconnected. It combines a projection-based update with dynamic average consensus to estimate both players’ actions and the aggregative term, recasting the problem as stability analysis of a time-varying nonlinear system. Using a time-varying Lyapunov function, the authors prove exponential convergence to the unique NE $\\bm{x}^*$, with limit values matching the consensus projection $P_n\\phi(\\bm{x}^*)$ and the dispersion term $\\alpha P_n^\\perp\\phi(\\bm{x}^*)$. This work extends constrained DNE results to switching networks, offering faster convergence and lower communication burden via a compact, 3Nn-state protocol that requires each node to exchange only $2n$-dimensional vectors with neighbors.
Abstract
The property of the communication network and the constraints on the strategic space are two factors that determine the complexity of the distributed Nash equilibrium (DNE) seeking problem. The DNE seeking problem of aggregative games has been studied for unconstrained case over all types of communication networks and for various types of constrained games over static and connected communication networks. In this paper, we investigate the DNE seeking problem for constrained aggregative games over jointly connected and weight-balanced switching networks, which can be directed and disconnected at every time instant. By integrating the projected gradient technique and the dynamic average consensus algorithm, we convert our problem to the stability problem of a well-defined time-varying nonlinear system. By constructing a time-varying Lyapunov's function candidate for this time-varying nonlinear system, we conduct a rigorous Lyapunov's analysis to conclude the exponential stability of this system and hence solve our problem.