A note on the ultimatum paradox, bounded rationality, and uncertainty

The ultimatum game is a sequential-move bargaining game in which a “giver” offers a “taker” a share of a monetary pie.  The predicted subgame perfect equilibrium is for rational givers to offer the smallest possible share, and for rational takers to accept.  The experimental evidence suggests that givers make more generous offers because they have a “taste for fairness.”  This note offers a somewhat different interpretation based on the assumption that the utility function of takers is characterized by bounded rationality, while the objective of givers is to offer the smallest share that will not be rejected, which is not known with certainty.  This suggests that proffered shares will be greater than the minimum predicted by purely rational behavior; that offers will be less than a half of the bargaining surplus; and that offers will become less generous as uncertainty about the taker’s reservation offer diminishes.