Thanksgiving and The Origins of Gratitude
Just about a week ago, we as a country celebrated Thanksgiving, a holiday whose purpose is apparent in its name. People gather around with their loved ones and express their gratitude to their benefactors while sharing a warm meal. This brings to question, why? Of course, it is a wholesome and admirable event, but what makes people give back at all? As it turns out, this phenomenon of national gratitude has been a subject of study of game theorists, and can be boiled down into graph theory and cascades.
Gratitude, often dubbed as “social glue”, evolved from the concept of reciprocity. Perhaps the more basic form in social groups is direct reciprocity, which involves helping the individual who has helped you. Such behavior was observed in experiments involving primates – chimpanzees were much more likely to help another chimpanzee if it had helped them in the past. This can be summed up as a two-node cyclical graph, rather simply. More interestingly, there is another form of reciprocity called spatial reciprocity. This involves the perpetuation of altruistic acts among a group of nodes to create a generally cooperative and strengthened network. This can be visualized in a class of students who are experts at different portions of the content – if each student helps each other student everyone is benefitted in the class. This perpetuation is inspired by a cascade: if each of n nodes carries on a favor with a probability p, there will be n altruistic walks of average length 1/(1-p) amongst the graph, increasing the graph’s net cooperativity (a factor to assess the strength of a network) by n/(1-p). To put it into perspective, if we take the limit of this as p approaches 1 (which would imply that each node definitely passes on the favor), the net benefit to the graph is infinite.
Together, direct and spatial reciprocity work hand-in-hand to create the phenomenon of upstream reciprocity – the idea of giving back to the person who has helped you – which game theorists equate to gratitude. Putting these concepts together, we see that the simple idea of giving back to an individual can have a chain reaction throughout the network, in turn strengthening the network and thus each individual involved. So next time someone does something for you, maybe think about doing something in return. The possible benefit is truly infinite.
Sources:
https://www.vice.com/en/article/nze49g/the-game-theory-of-thanksgiving
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2197219/
https://ggsc.berkeley.edu/images/uploads/GGSC-JTF_White_Paper-Gratitude-FINAL.pdf