On Oligopoly Spectrum Allocation Game in Cognitive Radio Networks with Capacity Constraints

TL;DR

This paper develops an oligopoly spectrum pricing model for cognitive radio networks with capacity constraints, proposing algorithms to find Nash Equilibria and analyzing their convergence and dynamic behaviors.

Contribution

It introduces two realistic models with capacity constraints, develops low-complexity algorithms for equilibrium computation, and analyzes dynamic price adaptation behaviors.

Findings

Unique Nash Equilibrium solutions derived for both models

Algorithms converge quickly to equilibrium in simulations

Chaotic behaviors observed in dynamic price adaptation under certain conditions

Abstract

Dynamic spectrum sharing is a promising technology to improve spectrum utilization in the 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 fast 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.