Dynamic Price Competition between a Macrocell Operator and a Small Cell Operator: A Differential Game Model

Julián Romero,Luis Guijarro,Angel Sanchis-Cano

doi:10.1155/2018/1012041

Abstract

An economic model was analyzed where a new supplier implements the technology of the small cells and positions itself as an incumbent service provider. This provider performs a dynamic reuse of resources to compete with the macrocells service provider. The model was analyzed using game theory as a two-stage game. In the first stage, the service providers play a Stackelberg differential game where the price is the control variable, the existing provider is the leader, and the new supplier is the follower. In the second stage, users’ behavior is modeled using an evolutionary game that allows predicting the population changes with variable conditions. This paper contributes to the implementation of new technologies in the market of mobile communications through analysis of competition between the new small cell service providers (SSPs) and the existing service providers along with the users’ behavior of mobile communications. The result shows that users get a better service, SSP profits are guaranteed, and SSP entry improves users’ welfare and social welfare.

Highlights

Mobile communications have experienced an enormous growth and this tendency still continues as the number of connected users is higher every day
This paper proposes a business model where a service provider implements small cells technology (SSP) and competes against the existing macrocell provider or macrocells service provider (MSP)
The limitations of this technology were taken into accounts such as limited availability and coverage, dynamic reutilization of resources, and the decisions of users and service providers, while taking into consideration the influence of each provider over the decisions of their competitor

Summary

Introduction

Mobile communications have experienced an enormous growth and this tendency still continues as the number of connected users is higher every day. This paper is focused on the solutions provided by HetNets and, on one of its key elements: the small cells technology: micro-, pico-, and femtocells [2] This technology has been developed and deployed over the latest years making use of small stations connected to the Internet able to capture the signal of users and route the calls towards the mobile network [3], achieving significant improvements in data speed, availability, and coverage [4, 5]. In our paper a new service provider (SP) implements the technology of small cells to compete with the MSP for the users with a dynamic price control variable, the SSP resources vary over time, and the evolutionary users’ behaviors regarding subscribing the SP are analyzed.

Model Description

Game Analysis

Stage II

Stage I

Results and Discussion

Conclusions