Dynamic rate allocation in Markovian quasi-static multiple access channels

We deal with multiple access channels in which the channel coefficients follow a quasi-static Markov process on a finite set of states. We first show how to allocate the rates in a global optimal fashion, in each state of the process. We give a sufficient condition under which the optimal rates adhere to some fairness criteria, holding in a time consistent fashion. Then, we borrow two concepts from dynamic cooperative game theory, i.e. the Time Consistent
Core and the Cooperation Maintaining sets, which measure users' satisfaction with the assigned rate. We show that the sets of rates fulfilling these properties coincide, and they also coincide with the set of global optimal rate allocations.