The amplified and forwarded cooperative communication scheme is modeled using the Stackelberg market structure, in which the relay is willing to sell its resources; power and bandwidth to multiple users in the system to maximize revenue. The relay determines prices for transmitting user information based on available resources and user requests. Next, each user maximizes their utility function by determining the optimal power and optimal bandwidth to purchase from the relay. The user utility function is formulated as a joint concave function of power and bandwidth. The existence and uniqueness of the Nash equilibrium are studied using the exact potential game associated with the proposed utility function. The optimal solution (Nash equilibrium) can be obtained in a centralized way, which requires full knowledge of all channel conditions and seems impractical. Therefore, a distributed algorithm can be applied to obtain the solution with minimal information exchange between the relay and the users. The convergence of the algorithm is studied using the Jacobian Nashequilibrium matrix. Furthermore, optimal prices for power and bandwidth can also be achieved in a distributed manner. Numerical simulations are used to verify the validation of distributed algorithms. The amplified and relayed cooperative communication scheme is modeled using the Stackelberg market structure, in which the relay is willing to sell its resources; power and bandwidth to multiple users in the system to maximize revenue. The relay determines prices for transmitting user information based on available resources and user requests. Subsequently, each user maximizes the...... half of the paper ......er 6, 2006.[29] T. Basar and R. Srikant, “Revenue-maximizing pricing and capacity expansion in a many-users regime,” in INFOCOM 2002. Twenty-first annual joint conference of the IEEE Computer and Communications Societies. Acts. IEEE, vol. 1, 2002, pp. 294 – 301.[30] M. Hayajneh and C. Abdallah, “Distributed joint rate and power control game theory algorithms for wireless data,” CommunicationsLetters, IEEE, vol. 8, no. 8, pp. 511 – 513, Aug. 2004.[31] H. N. Agiza, G.-I. Bischi and M. Kopel, “A multistability in a dynamic Cournot game with three oligopolists,” Mathematics and Computersin Simulation, vol. 51, pp. 63–90, 1999.[32] N. Feng, S.-C. Mau and N. B. Mandayam, “Power pricing and control for network-centric and user-centric joint radio resource management,” Communications, IEEE Transactions on, vol. 52, no. 9, pp. 1547 – 1557, Sept. 2004.
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