On the Asymptotic Behavior of Selfish Transmitters Sharing a Common Channel

TL;DR

This paper studies the long-term behavior of selfish transmitters in a shared wireless channel, revealing conditions for convergence and characterizing the equilibrium distribution as a mixture of Poisson and Bernoulli distributions.

Contribution

It provides a necessary and sufficient condition for convergence and characterizes the asymptotic distribution at Nash equilibrium in multi-transmitter networks.

Findings

Convergence condition for total packet arrivals established

Asymptotic distribution is a mixture of Poisson and Bernoulli distributions

Insights into equilibrium behavior in large-scale selfish networks

Abstract

This paper analyzes the asymptotic behavior of a multiple-access network comprising a large number of selfish transmitters competing for access to a common wireless communication channel, and having different utility functions for determining their strategies. A necessary and sufficient condition is given for the total number of packet arrivals from selfish transmitters to converge in distribution. The asymptotic packet arrival distribution at Nash equilibrium is shown to be a mixture of a Poisson distribution and finitely many Bernoulli distributions.