The promise of providing anytime and anywhere multimedia services demands a large spectrum for broadband wireless communications. On one hand, this drives the advance of radio technology to faster, convenient and reliable communications. On the other hand, the enormous demand also unveils the problem of insufficiency and under-utilized ineffi-ciency of current radio spectrum. Useful radio spectrum is a scarce resource in that the characteristic of spectrum on different frequency is different, e.g. the communication on 60 GHz is only suitable for short distance because of the absorption of radio signal by oxygen of the Atmosphere. Nowadays, the most useful spectrum band for median and long distance communication is below 5 GHz due to the characteristic of spectrum and current circuit technology. To tackle the problem, the idea of exploiting under-utilized licensed spectrum for more flexible and efficient transmissions is receiving significant at-tentions lately. In particular, the concept of cognitive radio (CR) [4] is considered as a promising technique to improve the efficiency of current radio spectrum.
A cognitive radio (CR) is a software-defined radio capable of intelligently sensing, adapting and responding to constantly varying environments, particularly the available spectrum temporarily not used by licensed users. However, there still exist many technical challenges before cognitive radios can be practically deployed. One critical challenge is how to invite the licensed service operators to accept coexistence with cognitive users so that they are willing to share their unused spectrum to unlicensed cognitive (secondary) services. Leasing available spectrum to unlicensed services is an attractive solution that provides an incentive for legitimate licensed operators to support deploying cognitive radios [3]. This gains monetary profits for licensed operators, while fulfilling unlicensed services’ satisfaction requirements by renting.
1.2.1 Why Game Theory?
Conventional Media Access Control (MAC) theory is based on optimization, and the ob-jective function it aims at optimizing is the network system utility or the network system utility in terms of fairness, e.g. proportional fairness. Although some problem
formula-tions using optimization theory can be decomposed to problems to optimize network and user utility separately by dual-primal method [5], which makes distributed decision mak-ing possible, the solution for the optimization problem inherently couldn’t always satisfy each user’s individual utility.
In contrast to optimization-based approach, game theory is a mathematical tool to deal with interactions between multiple entities, each of which has its own utility function, and intrinsically looks for equilibrium solutions that maximizes each user’s individual utility. Though the network system utility may not be optimized, the strategy obtained from the game theoretical perspective provides a solution that achieves efficiency and fairness under certain criteria.
1.2.2 Related Work and Our Approach
An overview of the general idea and recent developments about dynamic spectrum shar-ing games can be found in [6]. The auction mechanism for spectrum band in CR networks with multiple primary and multiple secondary users is considered in [7], where the authors discuss competitive equilibrium, cheating behaviors which may deteriorate the efficiency of of the spectrum sharing and propose using reserve prices and beliefs to prevent collu-sion. The work in [8] and [9] consider a game model which incorporates both monetary gain and quality-of-service (QoS) satisfaction of wireless services in utility functions. The authors in [9] explicitly model the price for available bandwidth as a function of demand, and obtain the Nash equilibrium (NE) for the spectrum sharing strategy in a network con-sisting of a single primary service (PS) and multiple secondary services (SS). The work in [8] considers the spectrum trading game in a CR network with multiple PS’s and a single SS, and models the utilities of the PS and SS separately, wherein the demand of SS implicitly affects the price. However, under certain circumstances, the equilibrium band-width demand for the SS would be negative, and the corresponding NE turns out to be infeasible, though theoretically solvable. The work in [10] discusses the same problem as in [8], and compare different features such as market equilibrium as well as competitive and cooperative pricing strategies. In [11], the authors investigate the spectrum trading behaviors with a more general model in which multiple primary users (PUs) and
multi-ple secondary users (SUs) are considered in the CR network. However, the utility model considered in [11] may not capture different QoS requirements of SUs and assumes that each PU sets the same price for all SUs. One key assumption underlying all the above work is that each player in the modeled game have complete knowledge about the other players’ private information. This is in general not a realistic assumption. To account for the unknown private information within each player, one can resort to tools in Bayesian game or stochastic game to study the behaviors of spectrum trading in a sequential (dy-namic) manner [12, 13]. In [12], we formulate the spectrum trading behaviors for a CR network with multiple PS’s and a single SS as a Bayesian game, and study the correspond-ing solution concept, i.e. the perfect Bayesian equilibrium, sequentially. The work in [13]
proposes to characterize the dynamics of spectrum access strategies under a stochastic game framework with the introduction of state transitions. The authors also propose to predict the future dynamics using approaches in learning theory in order to obtain better strategies for spectrum bidding.
In this work, extending the studies in [12], we address the problem of spectrum trad-ing in a CR network consisttrad-ing of multiple PS’s and multiple SS’s. We assume each player (PS or SS) in the game has its own private information, such as the number of active connections within each service or the channel conditions, that is unknown to other players. With the assumption, we formulate a multistage trading model based on the Bayesian game to statistically account for the unknown private information (incomplete information), and sequentially obtain the perfect Bayesian equilibrium (PBE) in the trad-ing process. We further assume that each PS is allowed to set different prices to the SS’s with different QoS, and SS’s with different QoS can demand different bandwidth sizes to a particular PS in the considered model. Particularly, we consider a bandwidth constraint on the aggregate bandwidth demand from all SS’s such that the total demand has to be within feasible supply regions provided by each PS.