  We consider a situation where wireless service providers compete for
heterogenous wireless users. The users differ in their willingness to pay as
well as in their individual channel gains. We prove existence and uniqueness of
the Nash equilibrium for the competition of two service providers, for a
generic channel model. Interestingly, the competition of two providers leads to
a globally optimal outcome. We extend some of the results to the case where
more than two providers are competing. Finally, we provide numerical examples
that illustrate the effects of various parameters on the Nash equilibrium.
