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This paper presents a distributed power allocation (PA) algorithm for the downlink of relay enhanced cellular networks. The PA problem is built into a non-cooperative game where a utility function is formulated and maximized. The utility function is comprised of two parts considering the interests of the node B and the relay node respectively, which facilitates the distributed PA on the nodes. Since the relay user's data rate is constrained by the minimum capacity of the two hops, a novel pricing function is developed to avoid allocating excess power to the second hop when the capacity is inferior in the first hop. The proposed game theoretic approach is compared with the uniform power allocation and the pure iterative water-filling method. Simulation results show that within a few steps of iteration, the proposed scheme can not only achieve the highest system capacity, but also efficiently balance the capacities of relay …