Many social judgments hinge on assigning responsibility to individuals for their role in a group's success or failure. Often the group's success depends on every team member acting in a rational way. When someone does not conform to what others expect of them, cooperation breaks down. We present a computational model of responsibility judgments for individuals in a cooperative setting. We test the model in two behavioral experiments where participants were asked to evaluate agents acting in a cooperative, one-shot game. In Experiment 1, we show that participants' action predictions are consistent with a recursive reasoning model. In Experiment 2, we show that people's assignments of blame are influenced by both an agent's presumed rationality, or adherence to an expected policy, as well as the pivotality of the agent's actions, or how close the situation was to one in which the action would have made a difference to the outcome.