A distributed proximal-point algorithm for Nash equilibrium seeking under partial-decision information with geometric convergence

We consider the Nash equilibrium seeking problem for a group of noncooperative agents, in a partial-decision information scenario. First, we recast the problem as that of finding a zero of a monotone operator. Then, we design a novel fully distributed, single-layer, fixed-step algorithm, which is a suitably preconditioned proximal-point iteration. We prove its convergence to a Nash equilibrium with geometric rate, by leveraging restricted monotonicity properties, under strong monotonicity and Lipschitz continuity of the game mapping. Remarkably, we show that our algorithm outperforms known gradient-based schemes, both in terms of theoretical convergence rate and in practice according to our numerical experience.