The assignment of the computation and communication is one of the important problems in the design of peer-to-peer (P2P) Massively Multi-player Online Game (MMOG). A reputation mechanism for P2P MMOG is proposed in this paper to avoid the problems in P2P design. The communications among peers are described by whether the messages are received timely and correctly in the process of synchronization, and then the reliabilities of peers are quantified. The concept of local reputation is proposed, based on which the adaptive adjusting algorithm for the function of peers and the algorithm for getting update peer selecting reliable computing peers are brought forward to assign the computation and communication of the system. According to the experiments, the algorithms are effective for the distribution of the computation and communication.