On the Asymptotic Behavior of Selfish Transmitters Sharing a Common Channel

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.