Recommender system has been deployed in a large amount of real-world applications, profoundly influencing people's daily life and production.Traditional recommender models mostly collect as comprehensive as possible user behaviors for accurate preference estimation. However, considering the privacy, preference shaping and other issues, the users may not want to disclose all their behaviors for training the model. In this paper, we study a novel recommendation paradigm, where the users are allowed to indicate their "willingness" on disclosing different behaviors, and the models are optimized by trading-off the recommendation quality as well as the violation of the user "willingness". More specifically, we formulate the recommendation problem as a multiplayer game, where the action is a selection vector representing whether the items are involved into the model training. For efficiently solving this game, we design a tailored algorithm based on influence function to lower the time cost for recommendation quality exploration, and also extend it with multiple anchor selection vectors.We conduct extensive experiments to demonstrate the effectiveness of our model on balancing the recommendation quality and user disclosing willingness.