Competition of Wireless Providers for Atomic Users

TL;DR

This paper models competition among wireless providers for heterogeneous users using a multi-leader-follower game, proving equilibrium existence, uniqueness, and optimality conditions, along with a decentralized convergence algorithm.

Contribution

It introduces a comprehensive game-theoretic model for wireless provider competition with heterogeneous users, establishing equilibrium properties and a decentralized solution method.

Findings

Unique subgame perfect Nash equilibrium exists and is proven to be globally optimal.

Most users connect to only one provider at equilibrium.

The decentralized algorithm converges globally using only local information.

Abstract

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.