  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.
