Existing activity-based models are typically concerned with predicting observed aggregate activity-travel patterns. The interaction and dependencies between individuals have received less attention. Considered here is how one specific schedule choice, namely, the start time of an activity chosen by an agent, aggregates to form an equilibrium distribution, which in turn influences individual decision making. These choices are formalized as the outcomes of a game of incomplete information in which agents have to conjecture the behavior of other agents. The properties of the model are examined by using numerical computer simulations. The results of the simulations support the face validity of the formulated model.