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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. Even though games of this type have been the subject
of considerable study in the literature, 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.Comment: 18 pages, 4 figures, submitted to Valuetools '1
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