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

TL;DR

This paper investigates Nash equilibrium seeking in scenarios with limited information exchange, establishing conditions for convergence of algorithms even with non-smooth, non-Lipschitz game mappings.

Contribution

It characterizes the relationship between monotonicity and smoothness conditions and proves convergence of a proximal point algorithm under restricted monotonicity.

Findings

Established relations between monotonicity and smoothness conditions.

Proved convergence of a preconditioned proximal point algorithm.

Allowed for non-Lipschitz, non-continuous game mappings.

Abstract

We address Nash equilibrium problems in a partial-decision information scenario, where each agent can only exchange information with some neighbors, while its cost function possibly depends on the strategies of all agents. We characterize the relation between several monotonicity and smoothness conditions postulated in the literature. Furthermore, we prove convergence of a preconditioned proximal point algorithm, under a restricted monotonicity property that allows for a non-Lipschitz, non-continuous game mapping.