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We study a problem where wireless service providers compete for heterogenouswireless users. The users differ in their utility functions as well as in theperceived quality of service of individual providers. We model the interactionof an arbitrary number of providers and users as a two-stagemulti-leader-follower game. We prove existence and uniqueness of the subgameperfect Nash equilibrium for a generic channel model and a wide class of users'utility functions. We show that the competition of resource providers leads toa globally optimal outcome under mild technical conditions. Most users willpurchase the resource from only one provider at the unique subgame perfectequilibrium. The number of users who connect to multiple providers at theequilibrium is always smaller than the number of providers. We also present adecentralized algorithm that globally converges to the unique systemequilibrium with only local information under mild conditions on the updaterates.

Competition of Wireless Providers for Atomic Users