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

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.