A stackelberg game for pricing uplink power in wide-band cognitive radio networks

We study the problem of pricing uplink power in wide-band cognitive radio networks under the objective of revenue maximization for the service provider and while ensuring incentive compatibility for the users. User utility is modeled as a concave function of the signal-to-noise ratio (SNR) at the base station, and the problem is formulated as a Stackelberg game. Namely, the service provider imposes differentiated prices per unit of transmitting power and the users consequently update their power levels to maximize their net utilities. We devise a pricing policy and give conditions for its optimality when all the users are to be accommodated in the network. We show that there exist infinitely many Nash equilibrium points that reward the service provider with the same revenue. The pricing policy charges more from users that have better channel conditions and more willingness to pay for the provided service. We then study properties of the optimal revenue with respect to different parameters in the network. We show that for regimes with symmetric users who share the same level of willingness to pay, the optimal revenue is concave and increasing in the number of users in the network. We analytically obtain achievable SNRs for this special case, and finally present a numerical study in support of our results.

[1]  Eitan Altman,et al.  A survey on networking games in telecommunications , 2006, Comput. Oper. Res..

[2]  Eitan Altman,et al.  CDMA Uplink Power Control as a Noncooperative Game , 2002, Wirel. Networks.

[3]  Steven H. Low,et al.  Optimization flow control—I: basic algorithm and convergence , 1999, TNET.

[4]  T. Başar,et al.  A Stackelberg Network Game with a Large Number of Followers , 2002 .

[5]  Richard J. La,et al.  Window-based congestion control with heterogeneous users , 2001, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213).

[6]  Frank Kelly,et al.  Rate control for communication networks: shadow prices, proportional fairness and stability , 1998, J. Oper. Res. Soc..

[7]  T. Başar,et al.  Incentive-Based Pricing for Network Games with Complete and Incomplete Information , 2007 .

[8]  Allen B. MacKenzie,et al.  Using Game Theory to Analyze Physical Layer Cognitive Radio Algorithms , 2005 .

[9]  Yong Liu,et al.  Pricing in multiservice loss networks: static pricing, asymptotic optimality, and demand substitution effects , 2002, TNET.

[10]  Joseph Mitola,et al.  Cognitive Radio Architecture , 2006 .

[11]  Narayan B. Mandayam,et al.  Pricing and power control for joint network-centric and user-centric radio resource management , 2004, IEEE Transactions on Communications.

[12]  T. Basar,et al.  Differentiated Internet pricing using a hierarchical network game model , 2004, Proceedings of the 2004 American Control Conference.

[13]  Murat Alanyali,et al.  Loss-cognizant pricing in networks with greedy users , 2007, Comput. Networks.