Fast generalized Nash equilibrium seeking under partial-decision information

We address the generalized Nash equilibrium seeking problem in a partial-decision information scenario, where each agent can only exchange with some neighbors, although its cost function possibly depends on strategies of all agents. The few existing methods build projected pseudo-gradient dynamics, and require either double-layer iterations or conservative conditions step sizes. To overcome both these flaws improve efficiency, we design first fully-distributed single-layer algorithms based proximal best-response. Our schemes are fixed-step allow for inexact updates, which is crucial reducing computational complexity. Under standard assumptions game primitives, establish convergence to variational (with linear rate games without coupling constraints) by recasting our as proximal-point methods, opportunely preconditioned distribute computation among Since analysis hinges restricted monotonicity property, also provide new general results that significantly extend domain applicability methods. Besides, operator-theoretic approach favors implementation provably correct acceleration further speed. Finally, potential demonstrated numerically, revealing much faster respect validating theoretical findings.