Competition Between Wireless Service Providers: Pricing, Equilibrium and Efficiency

TL;DR

This paper models the competitive dynamics of wireless service providers using a Stackelberg game, analyzing monopoly and oligopoly scenarios to understand their effects on social welfare and profits.

Contribution

It introduces a game-theoretic framework to compare monopoly and oligopoly models in wireless markets, deriving equilibrium conditions and efficiency metrics.

Findings

Nash equilibrium exists and is unique under certain conditions.

The lower bound of the price of competition on social welfare is 3/4.

The lower bound of the price of competition on profits is 1.

Abstract

As the communication network is in transition towards a commercial one controlled by service providers (SP), the present paper considers a pricing game in a communication market covered by several wireless access points sharing the same spectrum and analyzes two business models: monopoly (APs controlled by one SP) and oligopoly (APs controlled by different SPs). We use a Stackelberg game to model the problem: SPs are the leader(s) and end users are the followers. We prove, under certain conditions, the existence and uniqueness of Nash equilibrium for both models and derive their expressions. In order to compare the impact of different business models on social welfare and SPs' profits, we define two metrics: PoCS (price of competition on social welfare) and PoCP (price of competition on profits). For symmetric cross-AP interferences, the tight lower bound of PoCS is 3/4, and that of PoCP is 1.