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. Experimental trials conducted during the last three decades have demonstrated, however, that proffered shares are more generous, presumably because givers have a “taste for fairness.” This note offers the alternative interpretation that the utility functions of takers are characterized by bounded rationality and the objective of givers is to offer the smallest share that will not be rejected. The dilemma confronting givers is that the reservation offer of takers is not known with certainty