Price competition between a macrocell and a small-cell service provider with limited resources and optimal bandwidth user subscription: a game-theoretical model

The ever-increasing demand for higher data rates in wireless commutations provides a rationale for small cells deployment. While the physical and technological aspects of small-cell networks have been extensively studied in recent years, the economic analysis has received much less attention. We focus on the economic rationale for a small-cell service provider (SSP) operating a market where an incumbent macrocell service provider (MSP) exists, and competition develops. We analyze such scenario for the case of fixed users by means of Game Theory, specifically through a two-stage game: in the first stage each service provider posts its price according to a Stackelberg game where the MSP is the leader and the SSP is the follower; and, in the second stage, each user chooses both which provider to subscribe to and the optimal amount of bandwidth. A subgame perfect Nash equilibrium is used as a solution concept, and it is derived analytically. We show that the SSP has an incentive to operate in the market and its profit gets higher as SSP’s resources increase. Furthermore, users benefit from SSP’s operation, which may provide a rationale for a regulatory authority to grant the SSP access to the market, despite the fact that MSP’s profit is harmed. Finally, we identify two modes of operation of the system, which depend on the SSP coverage: one where SSP’s deployment is limited and the MSP strategy is not affected by SSP competition and takes only the users outside the SSP coverage; and another, where the SSP covers a large area and the MSP competes against the SSP taking a fraction of the users inside the small cells.