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…show more content…
The relay re-encodes the decoded message and then forwards it to the destination node [5]–[7]. The authors in [3], developed performance characterizations in terms of the outage events and the associated outage probabilities.
The average symbol error probability (SEP) of cooperative system is used to analyze the performance for various systems and channel models [7]. Single and multiple relay selection were investigated, and several SNR sub-optimum multiple relay selection schemes with linear complexity in the number of the relays were proposed in [8].
Game theory is a powerful tool to study interaction among self interested users, it is most used in economics, operations research, political science, etc. [9]. In communication systems and networks game theory has been recently used extensively to model routing, flow control and power control in up-link CDMA systems, etc. [10]–
[14]. Conditions for the existence and the uniqueness of an equilibrium for these models are investigated using the characteristics of the utility function (i.e., quasi-concave utility function guarantees the existence of Nash equilibrium [15], the set of pure Nash equilibria of a S-modular game is always non-empty, and the Nash set has a largest and smallest element [16]. Every finite potential game admits at least one Nash equilibrium, whereas for infinite potential games, sufficient

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