Fixed-Rate Equilibrium in Wireless Collision Channels

We consider a collision channel, shared by a finite number of self-interested users with heterogenous throughput demands. It is assumed that each user transmits with a fixed probability at each time slot, and the transmission is successful if no other user transmits simultaneously. Each user is interested in adjusting its transmission rate so that its throughput demand is met. When throughput requirements are feasible, we show that there exist two equilibrium points where users satisfy their respective demands. In one equilibrium all users transmit at lower rates, compared to their transmission rates at the other equilibrium. This fact is meaningful in wireless systems, where lower transmission rates translate to power savings. Subsequently, we propose a distributed scheme that ensures convergence to the lower-rate equilibrium point. We also provide some lower bounds on the channel throughput that is obtained with self-interested users, both in the symmetric and non-symmetric case.