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Cooperative communication exploits wireless broadcast advantage to confront the severe fading effect on wireless communications. Proper allocation of power can play an important role in the performance of cooperative communication. In this paper, we propose a distributed game-theoretical method for power allocation in bidirectional cooperative communication networks. In this work, we consider two nodes as data sources who want to cooperate in sending data to the destination. In addition to being data source, each source node has to relay the other's data. We answer the question: How much power each node contributes for relaying other node's data? We use Stackelberg game which is an extensive-form game to find a solution to this problem. The proposed method reaches equilibrium in only one stage. It is shown that there are more benefits when bidirectional cooperation is done between node pairs who are closer to each other. Simulation results show that the proposed method leads to fair solution and the nodes farther to the destination should contribute more power to cooperate with others.