Relay power allocation in auction-based game approach

In this work, with respect to the uncertainty about the individual information, we investigate the relay power allocation problem from the energy-efficient, Pareto optimal, and competitive fairness perspective. At first, we design an easy-implementation energy efficiency metric, which aims at striking a balance between the QoS provisioning and the energy consumption. Then, an auction mechanism is proposed for relay power allocation. By transferring the auction mechanism into a game, we prove the existence, uniqueness, and Pareto optimality of the Nash equilibrium (NE) for our auction game, and show that the allocation strategies from the NE can achieve the energy efficiency in terms of the proposed metric. Next, we develop a distributed relay power allocation algorithm based on our best-response functions to reach the Pareto optimal NE. Importantly, we not only certify the convergence of the proposed algorithm, but also provide quantitative analysis on it. Extensive simulations results are conducted to confirm the validity of the analytical results.