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Owing to the evolution of green communications, energy efficiency is treated as an important performance metric of a uplink orthogonal frequency division multiple access (OFDMA) system. In this study, the authors propose an energy-efficient resource allocation scheme by using the correlated equilibrium (CE). At first, the authors construct an energy-efficient resource allocation game, where each subcarrier is viewed as a player to choose the most satisfying user, and the objective is to balance the tradeoff between the total energy efficiency and the fairness. Since the CE can achieve better performance by helping the non-cooperative players coordinate their strategies, the authors employ the CE to analyse the proposed game. Next, the authors derive the condition under which the CE is Pareto optimal and employ linear programming duality to show its closed-form expressions. Furthermore, the authors present a linear programming method and a distributed algorithm based on the regret matching procedure to implement the CE, respectively, which can help us determine the desired resource allocation. Simulation results demonstrate that our scheme is able to achieve good convergence, Pareto optimality and fairness.