We deal with multiple access channels whose channel coefficients follow a quasi-static Markov process on a finite set of states. We address the issue of allocating transmission rates to users in each time interval, such that optimality and fairness of an allocation are preserved throughout a communication, and moreover all the users are consistently satisfied with it. First we show how to allocate the rates in a global optimal fashion. We give a sufficient condition for the optimal rates to fulfil some fairness criteria in a time consistent way. Then we utilize the game-theoretical concepts of time consistent Core and Cooperation Maintenance. We show that in our model the sets of rates fulfilling these properties coincide and they also coincide with the set of global optimal rate allocations. The relevance of our dynamic rate allocation to LTE systems is also shown.