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A pricing-based non-cooperative game is proposed to stimulate cooperation and perform spectrum allocation in multi-relay cooperative transmission networks. The authors construct a buyers' market competition model to consider that multiple relays are willing to share their spectrum resources with a single user. Both the benefits of the relays and the user are concerned in the game. First, according to the current user's demand, the relays as sellers compete with each other to determine the price of relaying that can maximise their profits. Then to maximise its utility, the user purchases the optimal amount of spectrum resources from each relay. The existence of the Nash equilibrium (NE), that is, the solution of the game, is proved. Even though the NE can be obtained in a centralised manner, a distributed algorithm to search for the NE is developed, which is more applicable in practical systems. Also, the convergence conditions of the algorithm are also analysed. Furthermore, the authors have also proved that the NE is not efficient when considering the total relays' profits. Thus, a general method to find the global optimal solution that maximises the total relays' profits is given. Simulation results show, by using the game, that a reasonable spectrum allocation can be performed between the relays and the user.