The ultimatum game was first introduced to the literature by Güth, Schmittberger, and Schwarze . It is a one-shot two-stage sequential bargaining game. It is often used to illustrate the backward induction method of solving for a subgame perfect Nash equilibrium for monetary payoff maximizing players. However, the game involves salient fairness considerations and there are multiple reported results of equal-split or close to equal-split outcomes from experiments. Strategic considerations of the players include notions of fear, negative reciprocity, and other-regarding preferences.
In stage 1 of the ultimatum game the first player proposes a specific split of a fixed amount of money, say $10, to the second player. In stage 2 the second player can either accept the proposed split or reject it. If he/she accepts, the $10 is divided according to the first mover's proposal. If he/she rejects, both players get 0.
Overview of the Most Common Setup
Nash Prediction for Self-Regarding Preferences
The subgame perfect Nash equilibrium for agents with self-regarding preferences is for player 1 to propose keeping all the money for himself and by the tie-breaking rule for player 2 to accept because he/she will be indifferent between vetoing and accepting a proposal in which he/she receives a payoff of zero (or to pass the smallest possible positive amount of money, in this case $1 in the absence of the tie-breaking rule).
Common Experimental Results
Dickinson  in his classroom experiment reports that the players do not behave as predicted by the self-regarding preferences model. Instead, responders reject many positive offers and usually accept only close to equal-split proposals. The average offers to second movers in this classroom game vary from 27 to 37 percent of a pie. The results show that students? rejection frequency for the similar offer range goes up as the size of the
Possible Explanations of Observed Behavior
Player 1 may propose a positive amount for player 2 because of:
To test for quantitative effects of altruistic other-regarding preferences and fear of rejection of proposals one can use a dictator control treatment. For the description of Ultimatum Game Dictator Control go to the Dictator Game section.
Applications to Real-Life Situations
One offer and a rejection or acceptance in the Ultimatum Game is similar to final-stage negotiations of various sorts: