Conceptions of fairness guide individuals to share, even when different strategies exist that could create greater equality, according to a new Yale study bridging psychology and economics.

The study consisted of a two-player game in which participants could split money between themselves and another player who would receive a multiple of whatever the starting player gave. Participants logged onto Amazon’s Mechanical Turk, a website for people all over the world to complete short tasks that require human intelligence. They were given 10 cents and told that they could give whatever portion they wanted to another anonymous participant, who would in turn give back a portion of his or her own money. The choice was complicated when participants were informed that whatever they gave away would be multiplied by a factor of two or more, meaning that if the participant gave five cents, then 10 or more would be delivered to the other player. The player’s own pot of money was not multiplied by any factor. Twenty percent of participants favored the 50-50 split over mathematically fairer options, suggesting that their decisions were not based solely on reason.

“The people consistently giving half are making a mistake,” said David Rand, principal author of the study and Director of Yale’s Human Cooperation Laboratory. “They are applying a simple rule which often makes sense to a situation where it does not actually make sense.”

This simple rule, known as a heuristic, is a common phenomenon in economics. When faced with a common or urgent problem, it is not always possible or convenient to deliberate on a solution.

According to Jillian Jordan GRD ’19, a psychology student and one of the study’s authors, the inability to think long and hard often leads people to a heuristic, or “a quick way of making a decision that may not be particularly systematic.”

“It may not have a strict algorithm that takes all these inputs having to do with the payoffs of the game that comes up with the rational, best outcome,” she said. “Rather, it’s the sort of rapid, gut response that says, ‘in general, I’m going to do this type of thing.’”

If the players desire selfish outcomes, they should give nothing, and if they are altruistic, they should give everything, Jordan said. The study did find strong concentrations at either end of the spectrum, but also found a concentration consistently in the middle, suggesting a third way of thinking about the game.

This trimodal, or triple-concentrated, distribution is a significant contribution of the study to the literature on game theory, said Gilbert Skillman, professor of economics at Wesleyan University. He argued that the third distribution lends credence to both of the main arguments against the rational choice model — that people always make choices to get more rather than less of desirable things. Instead, he said, people have other preferences, an argument known as economic theory ignorance, and also do not have the time or wherewithal to consider all factors, but rather take shortcuts, an argument known as bounded rationality.

“What’s cool about this [finding] is that it opens up a way to understand that both things could be the case,” Skillman said. “The third mode … [is] the interesting contribution of this study compared to the standard results before. Because it looks like both things are going on … one, using a rule of thumb, but two, contributing to the public good, to some extent.”

Even without any time constraint, these participants did not follow strategies that would result in equal final distributions of cash, such as giving 20 percent of the starting money if the gift would be increased by a factor of four. Instead, they favored a 50–50 split of the starting cash no matter how high the multiplier effect rose.

These choices make some sense in a repeated game, but in this experiment, there was no expectation of reciprocity, Jordan said. It was a one-time game, with decisions made without knowledge of the other player’s choice.

According to Valerio Capraro, a post-doctoral researcher from the University of Southampton University and a co-author of the study, the next step in the research could be finding a way to describe the participants’ behavior when making heuristic decisions.

“It’s very difficult to model these people because every mathematical model you can think of would depend on the benefit, so increasing the benefit would change the prediction of the model — but here, nothing changes,” he said. “That’s a difficult point to explain from a mathematical point of view.”

The one-shot Prisoner’s Dilemma game, used frequently in game theory and psychology research, was formalized in 1992 by Albert W. Tucker, a Canadian mathematician and recipient of the 1980 John von Neumann Theory Prize.