An evolutionary game perspective to ALOHA with power control

We study a large population of communicating terminals using an ALOHA protocol with two possible levels of transmission power. We pose the problem of how to choose between these power levels. We study two non-cooperative optimization concepts: the Nash equilibrium and the Evolutionary Stable Strategy. The latter were introduced in mathematical biology in the context of Evolutionary Games, which allow to describe and to predict properties of large populations whose evolution depends on many local interactions, each involving a finite number of individuals. We compare the performances of these non-cooperative notions with the global cooperative solution. The payoffs that we consider are functions of the throughputs and of the cost for the power levels. We study in particular the impact of the pricing for the use of the power levels on the system performance.