  We study a problem where wireless service providers compete for heterogenous
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. We 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 the competition of resource providers leads to
a globally optimal outcome under mild technical conditions. Most users will
purchase the resource from only one provider at the unique subgame perfect
equilibrium. The number of users who connect to multiple providers at the
equilibrium is always smaller than the number of providers. We also present a
decentralized algorithm that globally converges to the unique system
equilibrium with only local information under mild conditions on the update
rates.
