​The Game Theory of Thanksgiving

Gratitude can unleash epidemics of altruism. Watch out, or you might be the next to get infected...with NICENESS!

Becky Ferreira

Becky Ferreira

“The First Thanksgiving at Plymouth” or “Not Enough Chairs for All the Native Americans.” Image: Jennie Augusta Brownscombe, 1914

Today, people all across the USA are united in the dual joys of gluttony and gratitude, the most noble of all pursuits. Thanksgiving is a holiday that doesn't need Linus van Pelt to explain away its meaning—the upshot is right there in its name. Despite its lugubrious origins, Thanksgiving has become yearly reminder to be grateful for the sacrifices others have made for our benefit, and to pay those good deeds forward.

That second feature of gratitude—the resolve to help others because you have been helped—is actually something of an evolutionary quagmire. Why does gratitude inspire people to help third parties, even strangers, who had nothing to do with the original altruistic acts?

Game theorists have given this impulse the delightful name "upstream reciprocity." In 2007, Martin Nowak and Sébastien Roch of Harvard University published the first mathematical model of it in The Proceedings of the Royal Society B.

Using random walks—which are models that chart a sequence of random steps—the researchers discovered that upstream reciprocity likely didn't evolve by itself, but rather blossomed as an extension of more basic forms of cooperation, such as direct and spatial (or network) reciprocity.

A representation of upstream reciprocity, which models how people pay it forward. Image: © 2006 The Royal Society

Direct reciprocity is summed up by the axiom that I'll scratch your back if you scratch mine. The cost-benefit analysis there is pretty straightforward, and so is the potential for upstream reciprocity to occasionally "hitch-hike," as Nowak and Roch put it, off of this basic cooperative activity.

Spatial reciprocity, on the other hand, has to do with chain reactions of random altruistic acts inspired by imitation. To illustrate the concept, Nowak and Roch created models with cooperative players, who would propagate helpful deeds upstream, and defectors, who try to game the system by accepting benefits, then neglecting to pass them on.

Some of the players were also programmed to imitate the successful strategies of their neighbors, and that is how upstream reciprocity really gained steam in the model. Think about it: if your neighbor is a defector, and you see what a sweet deal they are getting by accepting help but never offering it, you might want to copy them. But if all the neighbors around a defector mimic that behavior, the altruistic acts dry out tout suite.

However, copying a cooperator gives rise to random walks of upstream reciprocity. In this way, local feelings of gratitude inspire altruistic acts to essentially go viral, leading to a wave of cooperators helping third parties, even though those parties may not directly reciprocate.

A model of upward reciprocity arising from spatial reciprocity. Image: © 2006 The Royal Society.

This strengthens group cooperation considerably, which in turn benefits the individual, providing a strong case for upstream reciprocity's evolutionary emergence. In some models, there were even large cascade effects called "epidemiologies of altruism," which were characterized by "an explosive increase of altruistic acts," according to Nowak and Roch.

"For a change, this is a pandemic which would be welcomed by all of us," they added.

Indeed it would. Along those lines, we should all aspire to spark our own little epidemiologies of altruism this Thanksgiving, whenever we are not stuffing our faces. A little game theory can go a long way when it comes to spreading gratitude literally like the plague.