Oligopolistic spectrum allocation game via market competition under spectrum broker

For future dynamic spectrum access (DSA) systems, new spectrum management methodologies will be adopted such that the licensed primary spectrum holders can reallocate part of their available bandwidth to the unlicensed secondary service providers for profits, based on market-driven mechanisms. This is known as spectrum market or spectrum trading. This paper aims to propose a dynamic spectrum market model where each spectrum holder has a limited amount of spectrum and is allowed to enter a portion of its available bandwidth into the market managed by a spectrum broker, besides its primary services. To model the price dynamics, a continuous-time price adjustment process governed by a differential equation is considered. Subsequently, we show that the problem is a dynamic N-player oligopoly differential game, subject to the bandwidth constraint. We analyze the feedback Nash equilibrium (NE) solutions for the general game and provide a complete, closed-form solution for the special symmetric case. The solution can be characterized into three distinct regions and transitions between these regions may occur as time evolves, which will be thoroughly investigated. In addition, we propose a discrete-time price adjustment implemented at the spectrum broker. Extensive numerical studies are provided to investigate various aspects of the proposed competition.