We present an experiment designed to separate the two commonplace explanations for behavior in ultimatum games—subjects’ concern for fairness versus the failure of subgame perfection as an equilibrium refinement. We employ a tournament structure of the bargaining interaction to eliminate the potential for fairness to influence behavior. Comparing the results of the tournament game with two control treatments affords us a clean test of subgame perfection as well as a measure fairness-induced play. We find after 10 iterations of play that about half of all non-subgame-perfect demands are due to fairness, and the rest to imperfect learning. However, as suggested by models of learning, we also confirm that the ultimatum game presents an especially difficult environment for learning subgame perfection.