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We consider mobile robot navigation in dense human crowds. In particular, we explore two questions. Can we design a navigation algorithm that encourages humans to coop- erate with a robot? Would such cooperation improve navigation performance? We address the first question by developing a probabilistic predictive model of cooperative collision avoidance and goal-oriented behavior. Specifically, this model extends the recently introduced interacting Gaussian processes approach to the case of multiple goals and stochastic movement duration. We answer the second question by empirically validating our model in a natural environment (a university cafeteria), and in the process, carry out the first extensive quantitative study of robot navigation in dense human crowds (completing 488 runs). The “multiple goal” interacting Gaussian processes algorithm performs comparably with human teleoperators in crowd densities near 1 person/m2, while a state of the art noncooperative planner exhibits unsafe behavior more than 3 times as often as our planner. Furthermore, a reactive planner based on the “dynamic window” approach—widely used for robotic tour guide experiments—fails for crowd densities above 0.55 people/m2. We conclude that a cooperation model is critical for safe and efficient robot navigation in dense human crowds.