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This letter studies the joint relay selection (RS) and spectrum allocation (SA) problem for the multi-user and multi-relay (MUMR) cellular networks. Regarding the amount of spectrum resource that a relay is willing to contribute for a particular user as the cooperative strategy of the relay, the joint RS and SA problem can be formulated as a cooperative bargaining game. Since there exists a unique Nash bargaining solution (NBS) to the game, a Langrangian relaxation with iterative search approach is proposed to find the NBS. By comparing with the maximal-rate and the max-min based RS and SA schemes, simulation results show that the proposed bargaining game approach achieves a fair and efficient rates distribution among the competitive users in the Pareto optimal sense.