Linearly Coupled Communication Games

TL;DR

This paper analyzes linearly coupled multi-user communication games, characterizing equilibria, quantifying inefficiencies, and proposing conjectural equilibria to improve non-cooperative performance in applications like wireless access.

Contribution

It explicitly characterizes Nash and Pareto boundaries, quantifies the price of anarchy, and introduces conjectural equilibria with convergence analysis for linearly coupled communication scenarios.

Findings

Nash equilibrium and Pareto boundary are explicitly characterized.

The price of anarchy for non-cooperative strategies is quantified.

Conjectural equilibria can be stable and improve performance.

Abstract

This paper discusses a special type of multi-user communication scenario, in which users' utilities are linearly impacted by their competitors' actions. First, we explicitly characterize the Nash equilibrium and Pareto boundary of the achievable utility region. Second, the price of anarchy incurred by the non-collaborative Nash strategy is quantified. Third, to improve the performance in the non-cooperative scenarios, we investigate the properties of an alternative solution concept named conjectural equilibrium, in which individual users compensate for their lack of information by forming internal beliefs about their competitors. The global convergence of the best response and Jacobi update dynamics that achieve various conjectural equilibria are analyzed. It is shown that the Pareto boundaries of the investigated linearly coupled games can be sustained as stable conjectural equilibria if the belief functions are properly initialized. The investigated models apply to a variety of realistic applications encountered in the multiple access design, including wireless random access and flow control.