Evolutionary Games for Multiple Access Control

TL;DR

This paper models multiple access control as an evolutionary game, analyzing equilibrium properties, stability, and long-term dynamics, including hybrid channels and signaling strategies, to optimize system performance.

Contribution

It introduces a novel evolutionary game framework for multiple access control with coupled constraints and studies equilibrium stability and dynamics in complex communication scenarios.

Findings

Pure equilibria are Pareto optimal and resilient to coalitional deviations.

Evolutionary dynamics converge to equilibrium states in simulated examples.

Correlated strategies improve decision-making in single-receiver models.

Abstract

In this paper, we formulate an evolutionarymultiple access control game with continuousvariable actions and coupled constraints. We characterize equilibria of the game and show that the pure 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 specific equilibrium solution using the concepts of normalized equilibrium and evolutionarily 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, Smith dynamics and replicator dynamics. In addition, we examine correlated equilibrium for the single-receiver model. Correlated strategies are based on signaling structures before making decisions on rates. We then focus on evolutionary games for hybrid additive white Gaussian noise multiple access channel with multiple users and multiple receivers, where each user chooses a rate and splits it over the receivers. Users have coupled constraints determined by the capacity regions. Building upon the static game, we formulate a system of hybrid evolutionary game dynamics using G-function dynamics and Smith dynamics on rate control and channel selection, respectively. We show that the evolving game has an equilibrium and illustrate these dynamics with numerical examples.