On the Nash Equilibria of graphical games for channel access in multihop wireless networks

We study a multihop wireless network with a tree topology where selfish nodes compete for channel access. Firstly, we discuss how this is relevant to future multihop networks focusing on the concept of Device-to-Device communication. We then model this framework as a graphical game, which is a special case of a non-cooperative game in which the payoff of a node is influenced only by a subset of its neighbors. We discuss two payoff models that may be used depending on the application: The first focuses only on transmitters and assigns by default a zero payoff to the receivers and the second models a non-zero payoff to both transmitters and receivers. We then present a distributed scheme that finds an efficient Nash Equilibrium (NE) under both payoff models. We evaluate its performance through extensive simulations showing that the algorithm converges fast to a NE, in a number of rounds that is proportional to the logarithm of the number of nodes. Finally, we find that the number of successful transmissions is almost equal at any NE. This indicates that, under this metric, any NE is practically equally preferable.