Experiments in fairness

This is the ultimatum game: You are provisionally allocated USD10 with the following instructions. You have to decide a way to divide this money with another person. If she or he agrees, the division is carried out. If not, you both get nothing. What would you do? How would you react if you were the person receiving the offer?

The standard economic analysis says that the recipient accepts any positive amount (something is better than nothing) and that, knowing this, the proponent offers a division of 9.99-0.01. Kahneman et al. (1986) 1 put this game to the test and found that most proposers offer 5 to recipients and that offers of less than 5 are sometimes rejected.

Before rejecting the Homo oeconomicus and the standard economic theories one must consider that, as many other experiments show, selfishness is a good hypothesis to predict market behavior. Rather the question these experiments open is about when it is correct to assume a selfish behavior and when it is not. The question is complicated, as there is one way to be selfish, but there are many ways and reasons to be generous.

The explosion of research on this topic in the last two decades is overwhelming. Many researchers have explored the role of alternative social contexts, cultural differences (the experiments of Joe Henrich are most fascinating) and other possible emotions (pride, guilt, parochialism, reciprocity, altruism, spite, fairness or embarrassment to name a few). It is still too early to evaluate the success of this research. Some regularities start to show, but no comprehensive, accepted general theory has been developed yet. I will summarize three articles that illustrate some of the strategies this line of research has followed and also some of the difficulties to reach final conclusions.

In a relatively early work Forsythe et al. (1994) 2 replicate Kahneman et al. (1986)’sresults from the ultimatum game, and also study a different version of it: the dictator game, where there is a proponent and a recipient like in the ultimatum game, but where the recipient does nothing. Any offer the proponent makes is implemented. Of course, the Homo oeconomicus will decide to keep 100% of the money and share nothing, and indeed this is observed, but only 20% of the times. Another 20% of the times the division is 50-50, like in most of the ultimatum games. The generosity of the proponent still exists, although at a much lower level than in the ultimatum game. This implies that fairness alone cannot be the reason to give, or the results in the two games would have been the same. See Fig. 1 for the results.

Figure 1: Each histogram measures the amount of the proposal in dollars on the horizontal axis and the fraction of proposals of this amount on the vertical axis for the two dates when the experiment was conducted. In each of these experiments a total of USD 5 was allocated. The proposal is the money that is offered to the recipient. In the experiments without pay players allocated fictitious money. In the games with pay the money was real. | Credit: Forsythe et al. (1994)
Figure 1: Each histogram measures the amount of the proposal in dollars on the horizontal axis and the fraction of proposals of this amount on the vertical axis for the two dates when the experiment was conducted. In each of these experiments a total of USD 5 was allocated. The proposal is the money that is offered to the recipient. In the experiments without pay players allocated fictitious money. In the games with pay the money was real. | Credit: Forsythe et al. (1994)


To explore other motives for giving, the authors repeat the experiment framing the context. In one framing, there is no explicit division of the USD 10, but a take-it-or-leave-it offer made by a buyer to a seller. Say the seller values a good at USD 5 (the production cost) and that the buyer values it at USD 15 (her maximum willingness to pay). Knowing all this, the buyer is more willing to offer a price of 5 thus obtaining a benefit of 10 and leaving the seller with no profit. The same result is found if the proponent is told the story that he won the right to make the offer in a fair contest. More importantly, the recipient in the ultimatum game was also more willing to accept low offers.

In a further twist of the experiment, when in addition the proponent was urged to think how would he react to his own offer if he were the recipient, he was as generous as the subjects without the framing of the story. The authors suggest that reciprocity, rather than fairness, is behind these results.

Research continued along these lines. Hoffman et al. (1996) 3 conducted a series of experiments in which they isolated the proponent further and further form any social contact (from the recipient, other experimental subjects and the experimenter). In the most anonymous case, with double blind treatment, 64% of proposers take all 10 dollars and about 90% take at least 8.

After these and other experiments, a pattern emerges: the closer the experiment reflects the theoretical game (no social interactions, anonymity, market context) the closer the experiment reflects the theoretical equilibrium. A general theory of economic behavior needs to explain all the facts, the selfish market behavior and the seemingly altruistic preferences that are observed. But the first step is to identify the social contexts in which giving occurs and why. To some authors (and it is important to notice that many of these experiments have been designed and conducted with the collaboration of psychologists) the fact that social interactions make subjects more cooperative reinforces the evolutionary/reciprocity interaction rather than the fairness hypothesis. However, new research suggests that fairness may have not said its last word.

Some authors have explored the possibility that the fairness hypothesis can be defended in an evolutionary context. In one of the last works in this line of research, David et al. (2013) 4 retake the ultimatum game and study it using stochastic evolutionary game theory. The differences with the standard approach are twofold. First, in an evolutionary contest players of the game are not required to select their actions rationally, rather, actions come to them as traits selected in an evolutionary process. Second, the stochastic part of the analysis comes when agents are allowed to make mistakes when judging the payoffs and strategies of others. In this context, the authors find that natural selection favors fairness. More specifically the average strategy matches the observed behavior: proposers offer between 30% and 50%, and responders demand between 25% and 40%. Rejecting low offers increases relative payoff in pairwise competition between two strategies and is favored when selection is sufficiently weak. Offering more than you demand increases payoff when many strategies are present simultaneously and is favored when mutation is sufficiently high.

After the theoretical analysis the authors conduct an ultimatum game experiment with the added feature that players do not know with certainty the success of others. Their empirical findings follow the theoretical predictions: uncertainty about the success of others is associated with higher demands and offers. Fairness, after all, may be part of the explanation. The authors do not report on the dictator game, but one can conjecture that, as there is less uncertainty in this game (recall that the recipient does nothing, and that all offers made by the giver are automatically implemented), the fairness hypothesis could be compatible with the discrepancy of behavior in the two games.

Even if the evolutionary explanation is correct, there are still numerous questions to answer: why people obey their instincts rather than use their reason to play the game (is it costly to play against the instincts in terms of the time and effort needed to compute the best strategy or in terms of suffering a painful emotion?), and to what extend the evolutionary traits can be modeled by cultural interaction or by learning, are just two of them. We are witnessing the beginning of interesting developments in the understanding of economic behavior.



  1. Kahneman, Daniel; Knetsch, Jack L.; Thaler, Richard H. 1986. Fairness and the assumption of economics. Journal of Business59, 285–300.
  2. Forsythe, Robert; Horowitz, Joel; Savin, N.E.; Sefton, Martin 1994. Fairness in simple bargaining experiments. Games and Economic Behavior6(3), 347–369.
  3. Hoffman, Elizabeth; McCabe, Kevin; Smith, Vernon 1996. Social distance and other-regarding behavior indictator games. American Economic Review86(3), 653–660.
  4. Rand, David G.;Tarnita, Corina E.;Ohtsuki, Hisashi; Nowak, Martin A. 2013. Evolution of fairness in the one-shot anonymous Ultimatum Game. Proceedings of the National Academy of Sciences of the USA110(7), 2581–2586.

4 Comments 1 Trackback

Leave a comment


So… When facing a situation in which the Homo Oeconomicus does not only have to choose between a basket of goods but also on someone else’s income, a good named ‘fairness’ has to be added to the preference map. The same preference map that we give for granted and about which economics has almost nothing to say. 😉


José Luis FerreiraJosé Luis Ferreira

True, but adding goods to the preferences map can leave the theory without any explanatory power. The key is to understand when it is justified to add the “fairness good” and in what measure, thus the need to find regularities.

Diego MorenoDiego Moreno

Interesting comment about fairnes. Here’s a link that seem to suggest that aversion to inequality runs deep:

upworthy.com/2-monkeys-were-paid…happens-next? c=ufb1&goback=.gde_140296_member_186828930

José Luis FerreiraJosé Luis Ferreira

Thanks. Very interesting link. It seems to run deep indeed, at least deep in time as we seem to share this trait with our primate cousins.

Leave a reply

You may use these HTML tags and attributes: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>