Dynamic power allocation games in parallel multiple access channels

We analyze the distributed power allocation problem in parallel multiple access channels (MAC) by studying an associated non-cooperative game which admits an exact potential function. Even though games of this type have been the subject of considerable study in the literature [1–4], we find that the sufficient conditions which ensure uniqueness of Nash equilibrium points typically do not hold in this context. Nonetheless, we show that the parallel MAC game admits a unique equilibrium almost surely, thus establishing an important class of counterexamples where these sufficient conditions are not necessary. Furthermore, if the network’s users employ a distributed learning scheme based on the replicator dynamics, we show that they converge to equilibrium from almost any initial condition, even though users only have local information at their disposal.