This paper addresses the problem of optimal rate allocation for video stream in peer-to-peer networks. We present a distributed rate allocation algorithm with the goal of minimizing the total video distortion among peers receiving the same video. The scheme assumes that video streams can be transcoded/re- quantized at intermediate peers. We deploy a double pricing solution that simultaneously incorporates the network and the relay constraints in the peer-to-peer network and compare it with a single pricing solution where the relay constraint is applied only after all the communicating peers converge to optimality. We combine our solution with two video adaptation techniques: transcoding using times 264 and scalable coding using H.264 SVC (scalable video coding) extension. Our experiment shows that the double pricing solution consistently achieves a smaller aggregate distortion for all peers over the single pricing solution.