This paper applies quantal response equilibrium (QRE) models (McKelvey and Palfrey, 1995, Games and Economic Behavior) to ultimatum bargaining games. When the strategy space is discrete, as the noise vanishes, the QRE of the normal-form representation converges to a Nash equilibrium in which an equilibrium o er is between 0 and a half of the pie while the QRE of the extensive-form representatio...