This article studies how people reveal private information in strategic settings in which participants need to negotiate over resources but are uncertain about each other's objectives. The study compares two negotiation protocols that differ in whether they allow participants to disclose their objectives in a repeated negotiation setting of incomplete information. Results show that most people agree to reveal their goals when asked, and this leads participants to more beneficial agreements. Machine learning was used to model the likelihood that people reveal their goals in negotiation, and this model was used to make goal request decisions in the game. In simulation, use of this model is shown to outperform people making the same type of decisions. These results demonstrate the benefit of this approach towards designing agents to negotiate with people under incomplete information.