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

10/25/2019
by   Mattia Bianchi, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

06/23/2022

Nash equilibrium seeking under partial decision information: Monotonicity, smoothness and proximal-point algorithms

We address Nash equilibrium problems in a partial-decision information s...
06/30/2021

Distributed Nash Equilibrium Seeking under Quantization Communication

This paper investigates Nash equilibrium (NE) seeking problems for nonco...
02/22/2022

On the Rate of Convergence of Payoff-based Algorithms to Nash Equilibrium in Strongly Monotone Games

We derive the rate of convergence to Nash equilibria for the payoff-base...
03/20/2020

Fast generalized Nash equilibrium seeking under partial-decision information

We address the generalized Nash equilibrium (GNE) problem in a partial-d...
10/25/2019

A continuous-time distributed generalized Nash equilibrium seeking algorithm over networks for double-integrator agents

We consider a system of single- or double integrator agents playing a ge...
11/26/2019

Continuous-time fully distributed generalized Nash equilibrium seeking for multi-integrator agents

We consider a group of (multi)-integrator agents playing games on a netw...
08/13/2018

Distributed GNE seeking under partial-decision information over networks via a doubly-augmented operator splitting approach

We consider distributed computation of generalized Nash equilibrium (GNE...