We explore conditions under which behavior in a strategic setting can be rationalized as the best-response to some belief on other players’ behavior. We show that a restriction on preferences that we term quasi-monotonicity provides such a test for a family of ultimatum games. Preferences are quasi-monotone if an agent prefers an allocation that improves her payoff at least as much as that of others. In an experiment, we find that 94 percent of proposers make choices that are arbitrarily close to quasi-monotone preferences and beliefs. We indeed find that 64 percent of responders are consistent with quasi-monotone of preferences and 91 percent of responders make inconsistent choices in no more that 5 percent of decision problems. We find little support for convexity of preferences.