Revealed preferences and expectations: Evidence from ultimatum games

Behavior in the ultimatum game is modeled by exploiting standard nonparametric utility theory with the monotonicity assumption relaxed to a condition termed quasi-monotonicity. Proposers’ beliefs about responder behavior are likewise modeled nonparametrically, imposing only the restriction that proposers know responders have well-behaved, quasi-monotone preferences. Proposers are not assumed to be expected-utility maximizers. Their preferences over lotteries need only satisfy a much weaker condition. These assumptions suffice for player behavior to adhere to GARP, thus yielding straightforward testable implications in a completely nonparametric setting. Eighty three percent of proposers and sixty percent of responders make choices consistent with having rational, quasi-monotone preferences and beliefs. Tolerating infinitesimally small violations of rationality raises these proportions to ninety four percent and eighty percent, respectively. Our tests of well-behaved preferences and beliefs have high power against a variety of alternatives. We find strong evidence against convexity of preferences. Importantly, the failure of convexity is due to inconsistencies across games rather within games suggesting behavior consistent with menu-dependent preferences or beliefs. These experimental data imply restrictions that allow partial recovery of players’ preferences and beliefs which, in turn, yield informative nonparametric bounds on player behavior in counterfactual games of proposal and response. Finally, our approach suggests that the presence of rational behavior might informative in other games since its presence might require additional restrictions on preferences and/or beliefs. JEL classifications: