A Constrained Evolutionary Gaussian Multiple Access Channel Game

TL;DR

This paper models an evolutionary game for a Gaussian multiple access channel with continuous actions and rate constraints, analyzing equilibrium properties and stability under various dynamics.

Contribution

It introduces a novel evolutionary game framework for the Gaussian multiple access channel, characterizing equilibria and stability with respect to coalitional deviations.

Findings

Pure Nash equilibria are Pareto optimal and resilient to coalitional deviations.

The system's performance is analyzed using price of anarchy metrics.

Long-run behavior under different evolutionary dynamics is examined.

Abstract

In this paper, we formulate an evolutionary multiple access channel game with continuous-variable actions and coupled rate constraints. We characterize Nash equilibria of the game and show that the pure Nash equilibria are Pareto optimal and also resilient to deviations by coalitions of any size, i.e., they are strong equilibria. We use the concepts of price of anarchy and strong price of anarchy to study the performance of the system. The paper also addresses how to select one specifc equilibrium solution using the concepts of normalized equilibrium and evolutionary stable strategies. We examine the long-run behavior of these strategies under several classes of evolutionary game dynamics such as Brown-von Neumann-Nash dynamics, and replicator dynamics.