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This letter considers the problem of resource sharing between two selfish nodes in cooperative relay networks. In our system, each node can act as a source as well as a potential relay, and both nodes are willing to achieve an optimal signal-to-noise ratio (SNR) increase by adjusting their power levels for cooperative relaying. We formulate this problem as a two-person bargaining game, and use the Nash bargaining solution (NBS) to achieve a win-win strategy for both nodes. Simulation results indicate the NBS resource sharing is fair in that the degree of cooperation of a node only depends on how much contribution its partner can make to its SNR increase.