Resource allocation for AF cooperative communications using Stackelberg game

Amplify and forward (AF) cooperative communication scheme is modeled using Stackelberg market framework, where a relay is willing to sell its resources; power and bandwidth, to multiple users 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 bandwidth to buy from the relay. The existence and the uniqueness of the Nash equilibrium for given power and bandwidth prices are investigated using the concavity of the utility function, and the exact potential game associated with the proposed utility function. The Stackelberg Nash equilibrium is found using backward induction. A nested distributed algorithm is applied to obtain the Stackelberg-Nash equilibrium with minimum information exchange between the relay and users. Numerical simulations are used to verify the validation of the proposed framework.