A Unified Strategy for Solution Seeking in Graphical N-coalition Noncooperative Games

TL;DR

This paper introduces a unified, graph-based approach to efficiently find Nash equilibria in N-coalition noncooperative games, reducing communication and computation costs while ensuring convergence.

Contribution

It proposes an interference graph-based Nash equilibrium seeking strategy that unifies solution methods for various noncooperative game scenarios.

Findings

The strategy converges to a neighborhood of the Nash equilibrium.

It applies to special cases like single coalition or single agent.

Numerical examples validate the theoretical analysis.

Abstract

This paper aims to reduce the communication and computation costs of the Nash equilibrium seeking strategy for the $N$-coalition noncooperative games proposed in [1]. The objective is achieved in two manners: 1. An interference graph is introduced to describe the interactions among the agents in each coalition. 2. The Nash equilibrium seeking strategy is designed with the interference graphs considered. The convergence property of the proposed Nash equilibrium seeking strategy is analytically investigated. It is shown that the agents' actions generated by the proposed method converge to a neighborhood of the Nash equilibrium of the graphical $N$-coalition noncooperative games under certain conditions. Several special cases where there is only one coalition and/or there are coalitions with only one agent are considered. The results for the special cases demonstrate that the proposed seeking strategy achieves the solution seeking for noncooperative games, social cost minimization problems and single-agent optimization problems in a unified framework. Numerical examples are presented to support the theoretical results.