On oligopoly spectrum allocation game in cognitive radio networks with capacity constraints

Dynamic spectrum sharing is a promising technology to improve spectrum utilization in future wireless networks. The flexible spectrum management provides new opportunities for licensed primary user and unlicensed secondary users to reallocate the spectrum resource efficiently. In this paper, we present an oligopoly pricing framework for dynamic spectrum allocation in which the primary users sell excessive spectrum to the secondary users for monetary return. We present two approaches, the strict constraints (type-I) and the QoS penalty (type-II), to model the realistic situation that the primary users have limited capacities. In the oligopoly model with strict constraints, we propose a low-complexity searching method to obtain the Nash Equilibrium and prove its uniqueness. When reduced to a duopoly game, we analytically show the interesting gaps in the leader-follower pricing strategy. In the QoS penalty based oligopoly model, a novel variable transformation method is developed to derive the unique Nash Equilibrium. When the market information is limited, we provide three myopically optimal algorithms ''StrictBEST'', ''StrictBR'' and ''QoSBEST'' that enable price adjustment for duopoly primary users based on the Best Response Function (BRF) and the bounded rationality (BR) principles. Numerical results validate the effectiveness of our analysis and demonstrate the convergence of ''StrictBEST'' as well as ''QoSBEST'' to the Nash Equilibrium. For the ''StrictBR'' algorithm, we reveal the chaotic behaviors of dynamic price adaptation in response to the learning rates.