In order to encourage peers to contribute resources for P2P networks, the paper proposed an incentive mechanism to suppress whitewashing which is not overcome by reputation systems. Game-theoretic analysis reveals that the conventional Tit-for-Tat is not an evolutionary stable strategy in P2P systems including some whitewashers. It also indicates that an improved Tit-for-Tat integrating an appropriate identity cost is an effective strategy to defeat whitewashers. Simulation results show that 93 percent of peers can cooperate after nine cycles evolutions of the improved strategy when whitewashers are initially composed of 50 percent of peers in P2P systems.