Adaptive learning and a fairness motive we call "punishment" are the basis for two prominent and substantially different types of theories of ultimatum bargaining behavior. We compare adaptive learning and fairness in an experiment that involves punishment and reward versions of the ultimatum game. We draw conclusions concerning the abilities and limitations of both types of theories. The results shed light on how learning and fairness interact, information that should be useful in constructing a more comprehensive model. Journal of Economic Literature Classification Numbers: C78, C91, D83.