Modelling cooperation in a social network

Basically it seems that too much cooperation is self-destructive for maintaining an overall cooperative society, because you end up helping people who abuse your assistance. However the right amount of cooperation can be sustainable.

Which is near enough exactly what Plato was banging on about.


Examples of cooperation abound in nature, from honeybee hives to human families. Yet it's also easy enough to find examples of selfishness and conflict. Studying the conditions that give rise to cooperation has occupied researchers for generations, with implications for understanding the forces that drive workplace dynamics, charitable giving, animal behavior, even international relations.

A basic tenet of these studies is that cooperative behaviour arises when individuals interacting in a social network derive some benefit from being generous with one another. Yet social networks are not fixed. What if the structure of the network itself alters as individuals become more cooperative?

In a new report in the journal Nature Communications, Erol Akçay, an assistant professor of biology in Penn's School of Arts and Sciences, addresses this question of how an evolving social network influences the likelihood of cooperation in a theoretical social group. He finds that, although networks where connected individuals are closely related are more likely to cooperate, such groups can trigger a feedback loop that alters the structure of the network and leads to cooperation's collapse.

"We know from a half-century of study that cooperation is quite easy to evolve in principle," says Akçay, "in the sense that there are many, many sets of conditions that can make cooperative behaviors a better strategy than non-cooperative behaviour. So given that, why isn't the world a cooperative paradise? Because we know it isn't."

Akçay's theoretical work points to a reason why: It's possible that the social structure that gave rise to high levels of cooperation may not be stable in such a cooperative environment. Yet, his model also suggests that cooperation can be maintained if the benefits of generous behaviour are great enough.

The work builds upon studies that Akçay pursued with former postdoctoral researcher Amiyaal Ilany, now a faculty member at Bar-Ilan University. They developed a mathematical model of how individual animals inherit their social connections that can explain the structure of social networks in animal groups. In the new work, Akçay built on that earlier model by adding in an element of choice; individuals in the network could either connect with a parent's connection, or randomly with individuals aside from a parent's connections. The probabilities of making each type of connection determine the structure of the network.

Each individual in the model was further designated to be either a cooperator or a defector. Cooperators provide a benefit to those they connect with, but the total amount they provide is fixed, so the more connections they have, the less each connection receives. Both cooperators and defectors reap a benefit based on the number of links to cooperators they possess, but defectors don't offer anything in return"

https://www.eurekalert.org/pub_releases/2018-07/uop-uts071218.php