  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.
