Optimal random access in networks with two-way traffic

We consider a random access network in which the nodes need to optimize their channel access rates. The nodes are assumed to be rational and interested in their performance seen as a transmitter as well as a receiver. By casting this problem as a non-cooperative game, we derive conditions for the Nash equilibrium. We also show the existence of a Nash equilibrium when the nodes are constrained by their battery power (for this case, the constraints on the access rates of the nodes become coupled). For the special case where all nodes are each other's neighbors, we find that the equilibrium is given by the solution of a system of linear equations. An adaptive distributed scheme is then proposed for learning this equilibrium and its convergence is studied numerically.