Competition of wireless providers for atomic users: Equilibrium and social optimality

We study a problem where wireless service providers compete for heterogenous and atomic (non-infinitesimal) wireless users. The users differ in their utility functions as well as in the perceived quality of service of individual providers. We model the interaction of an arbitrary number of providers and users as a two-stage multi-leader-follower game, and prove existence and uniqueness of the subgame perfect Nash equilibrium for a generic channel model and a wide class of users' utility functions. We show that, interestingly, the competition of resource providers leads to a globally optimal outcome under fairly general technical conditions. Our results show that some users need to purchase their resource from several providers at the equilibrium. While the number of such users is typically small (smaller than the number of providers), our simulations indicate that the percentage of cases where at least one undecided user exists can be significant.