Correlated Anarchy in Overlapping Wireless Networks

We investigate the behavior of a large number of selfish users that are able to switch dynamically between multiple wireless access-points (possibly belonging to different standards) by introducing an iterated non-cooperative game. Users start out completely uneducated and naive but, by using a fixed set of strategies to process a broadcasted training signal, they quickly evolve and converge to an evolutionarily stable equilibrium. Then, in order to measure efficiency in this steady state, we adapt the notion of the price of anarchy to our setting and we obtain an explicit analytic estimate for it by using methods from statistical physics (namely the theory of replicas). Surprisingly, we find that the price of anarchy does not depend on the specifics of the wireless nodes (e.g., spectral efficiency) but only on the number of strategies per user and a particular combination of the number of nodes, the number of users and the size of the training signal. Finally, we map this game to the well-studied minority game, generalizing its analysis to an arbitrary number of choices.