Cheat-Proof and Optimal Access Controls in a Pairwise Interaction Network

We derive both the optimal and the game-theoretic (cheat-proof) solutions in closed form, to a problem of distributed access with power control in a pairwise interaction network. In this network, each node has an energy constraint in a fixed time unit for using different power levels in each access attempt competing with a randomly selected node. The one with larger power level wins the access. The optimal control for nodes in the network to maximize the number of wining the access as well as the game-theoretic (cheat-proof) control in which no one will deviate to attain higher number of wining the access are fully characterized in this paper.