Competitions and dynamics of duopoly wireless service providers in dynamic spectrum market

Dynamic spectrum access can significantly improve the spectrum utilization. For wireless service providers, the emergence of dynamic spectrum access brings new opportunities and challenges. The flexible spectrum acquisition gives a particular provider the chance to easily adapt its system capacity to fit end users' demand. However, the competition among several providers for both spectrum and end users complicates the situation. In this paper, we propose a general three-layer spectrum market model for the future dynamic spectrum access system, in which the interaction among spectrum holder, wireless service providers and end users are considered. We study a duopoly situation, where two wireless service providers participate in bandwidth competition in spectrum purchasing and price competition to attract end users, with the aim of maximizing their own profit. We believe we are the first one to explicitly study the relation of these two competitions in dynamic spectrum market. We formulate the wireless service providers' competition as a non-cooperative two-stage game. We first analyze the static game when full information is available for providers. Under general assumptions about the price and demand functions, a unique pure Nash equilibrium is identified as the outcome of the game, which shows the stability of the market. We further evaluate the market efficiency of the equilibrium in a symmetric case, and show that the gap with the social optimal is bounded within a small constant ratio. When the market information is limited, we provide myopically optimal adjustment algorithms for the providers. With such strategies, short term price updating converges to the Nash equilibrium of the given subgame, while long term bandwidth updating converges to a point close to the Nash equilibrium of the full game.