Ultimatum Game

Structure and theoretical prediction

The proposer makes a single offer of how much of, say, $100 to give the responder, who either accepts, in which case the money is split as proposed, or rejects, in which case both receive nothing. If every player maximizes only their own monetary payoff, the responder should accept any positive offer, so the subgame perfect equilibrium is for the proposer to offer the smallest possible amount. Rubinstein's (1982) alternating-offers bargaining model rests on the same rationality assumptions. Güth, Schmittberger and Schwarze (1982) were the first to design experiments testing this prediction directly with such a simple game.

Experimental results and fairness theories

In experiments, proposers typically offer 40 to 50 percent of the pie, and responders frequently reject low offers below about 20 to 30 percent. Thaler (1988) presented this as a leading anomaly in economics, and Kahneman, Knetsch and Thaler (1986) read it as evidence that people will bear costs to punish unfairness. Forsythe et al. (1994) compared it with the dictator game, in which the recipient cannot reject, showing that part of proposers' generosity stems from fear of rejection, while Hoffman et al. (1994) found that anonymity and how roles are assigned shift offers. Fehr and Schmidt (1999) and Bolton and Ockenfels (2000) explained the results by adding inequity aversion, a dislike of payoff differences between oneself and others, to the utility function.

Cross-cultural comparison and neuroeconomics

Roth et al. (1991) ran experiments in Jerusalem, Ljubljana, Pittsburgh and Tokyo and found systematic national differences in offers. Henrich et al. (2001) reported that mean offers across 15 small-scale societies ranged widely, from 26 to 58 percent, and that market integration and the everyday importance of cooperation explained much of the variation. Oosterbeek, Sloof and van de Kuilen (2004) quantified regional differences in a meta-analysis. In a functional MRI study, Sanfey et al. (2003) reported that unfair offers increased activity in the anterior insula and that this activity predicted rejection. Camerer (2003) synthesized these findings within the framework of behavioral game theory.

FAQ

What is the ultimatum game in simple terms?

One person proposes how to split some money; if the other accepts, they split it that way, and if the other rejects, neither gets anything. It shows that people often turn down unfair offers even at a cost to themselves.

How does it differ from the dictator game?

In the dictator game the recipient cannot reject. Comparing the two shows how much of a proposer's generosity reflects genuine concern for the other person and how much reflects worry about rejection.

Sources reviewed: 2026-10-26

References

1. Güth, W., Schmittberger, R., & Schwarze, B. (1982). An experimental analysis of ultimatum bargaining. Journal of Economic Behavior & Organization, 3(4), 367–388.
2. Rubinstein, A. (1982). Perfect equilibrium in a bargaining model. Econometrica, 50(1), 97–109.
3. Kahneman, D., Knetsch, J. L., & Thaler, R. H. (1986). Fairness and the assumptions of economics. Journal of Business, 59(4), S285–S300.
4. Thaler, R. H. (1988). Anomalies: The ultimatum game. Journal of Economic Perspectives, 2(4), 195–206.
5. Roth, A. E., Prasnikar, V., Okuno-Fujiwara, M., & Zamir, S. (1991). Bargaining and market behavior in Jerusalem, Ljubljana, Pittsburgh, and Tokyo: An experimental study. American Economic Review, 81(5), 1068–1095.
6. Forsythe, R., Horowitz, J. L., Savin, N. E., & Sefton, M. (1994). Fairness in simple bargaining experiments. Games and Economic Behavior, 6(3), 347–369.
7. Hoffman, E., McCabe, K., Shachat, K., & Smith, V. (1994). Preferences, property rights, and anonymity in bargaining games. Games and Economic Behavior, 7(3), 346–380.
8. Fehr, E., & Schmidt, K. M. (1999). A theory of fairness, competition, and cooperation. Quarterly Journal of Economics, 114(3), 817–868.
9. Bolton, G. E., & Ockenfels, A. (2000). ERC: A theory of equity, reciprocity, and competition. American Economic Review, 90(1), 166–193.
10. Henrich, J., Boyd, R., Bowles, S., Camerer, C., Fehr, E., Gintis, H., & McElreath, R. (2001). In search of homo economicus: Behavioral experiments in 15 small-scale societies. American Economic Review, 91(2), 73–78.
11. Camerer, C. F. (2003). Behavioral Game Theory: Experiments in Strategic Interaction. Princeton, NJ: Princeton University Press.
12. Sanfey, A. G., Rilling, J. K., Aronson, J. A., Nystrom, L. E., & Cohen, J. D. (2003). The neural basis of economic decision-making in the Ultimatum Game. Science, 300(5626), 1755–1758.
13. Oosterbeek, H., Sloof, R., & van de Kuilen, G. (2004). Cultural differences in ultimatum game experiments: Evidence from a meta-analysis. Experimental Economics, 7(2), 171–188.