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Cooperative communication has great potential to improve the transmit diversity in multiple users environments. To achieve a high network-wide energy-efficient performance, this letter poses the relay selection problem of cooperative communication as a noncooperative automata game considering nodes' selfishness, proving that it is an ordinal game (OPG), and presents a game-theoretic analysis to address the benefit-equilibrium decision-making issue in relay selection. A stochastic learning-based relay selection algorithm is proposed for transmitters to learn a Nash-equilibrium strategy in a distributed manner. We prove through the theoretical and numerical analysis that the proposed algorithm is guaranteed to converge to a Nash equilibrium state, where the resulting cooperative network is energy efficient and reliable. The strength of the proposed algorithm is also confirmed through comparative simulations in terms of energy benefit and fairness performances.