In this paper, a cooperative game is proposed to perform a fair and efficient resource allocation for the time division multiple access (TDMA) based cooperative communication networks. In the considered system, two selfish user nodes can act as a source as well as a potential relay for each other. A transmission node with energy limitation is willing to seek cooperative relaying only if the data-rate achieved through cooperation is not lower than that achieved without cooperation by consuming the same amount of energy. The cooperative strategy of a node can be defined as the number of data-symbols and power that it is willing to contribute for relaying purpose. We formulate this two-node fair and efficient resource sharing problem as a bargaining game. Since the Nash bargaining solution (NBS) to the game is computationally complex to obtain, a low-complexity algorithm to search the suboptimal NBS is proposed. Simulation results show that the NBS results are fair in that both nodes could experience better performance than if they work independently. And the NBS results are efficient in that the performance loss of the game to that of the maximal overall rate scheme is small while the maximal-rate scheme is unfair.