We study the selection of the rate allocation in multiple access channels (MAC). We consider MACs with different rate regions. Namely, we investigate the polytope rate regions, convex non-polytope rate regions, and non-convex rate regions. Different operating points of the rate region possess different properties in terms of efficiency, fairness, stability, etc. Our goal is to provide guidelines for the choice of an operating point using the above-mentioned criteria. We use two methodological approaches: fairness function approach leading to an optimal system operation point and game theoretic approach leading to an equilibrium point. In particular, we use games with correlated constraints. All fairness concepts and normalized Nash equilibrium produce the same rate allocation in the case of a MAC with polytope rate region. In the case of MACs with convex non-polytope and non-convex rate regions this property does not hold and behavior becomes much more various. In the case of some non convex rate regions the max-min fair allocation may even not exist.