Stackelberg Game for Joint Power and Bandwidth Allocations over Amplify and Forward (AF) Cooperative Communications

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Amplify and forward cooperative communication scheme is modeled using Stackelberg market framework, where

a relay is willing to sell its resources; power and bandwidth to multi-user in the system in order to maximize its

revenue. The relay determines the prices for relaying users’ information depending on its available resources and the

users’ demands. Subsequently, each user maximizes its own utility function by determining the optimum power and

the optimum bandwidth to buy from the relay. The utility function of the user is formulated as a joint concave function

of the power and the bandwidth. The existence and the uniqueness of the Nash equilibrium is investigated using the

exact potential game associated with the proposed utility function. The optimum solution (Nash equilibrium) can be

obtained in a centralized manner, which requires full knowledge of all the channel conditions and seems impractical.

Therefore, a distributed algorithm can be applied to obtain the solution with minimum information exchange between

the relay and the users. The convergence of the algorithm is investigated using the Jacobian matrix at the Nash

equilibrium. Furthermore, The optimum prices for the power and the bandwidth can also be obtained in a distributed

manner. Numerical simulations are used to verify the validation of the distributed algorithms.

Amplify and forward cooperative communication scheme is modeled using Stackelberg market framework, where

a relay is willing to sell its resources; power and bandwidth to multi-user in the system in order to maximize its

revenue. The relay determines the prices for relaying users’ information depending on its available resources and the

users’ demands. Subsequently, each user maximizes i...

... middle of paper ...

...er 6, 2006.

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