Helping out your neighbor or minding your own business? A challenging choice with different benefits for each decision. Game theory provides guidance in making such choices—from a theoretical perspective. Novel findings by Jakub Svoboda and Krishnendu Chatterjee at the Institute of Science and Technology Austria (ISTA) reveal new network structures that enhance cooperation throughout a system. These insights have potential applications also in biology.

Klosterneuburg/Austria, Dezember, 08th, 2024. The question of cooperation has puzzled scientists for a long time. Whether it is in the fields of biology, sociology, economics, or political science, finding out under which circumstance a group of individuals can be successful is crucial. Game theory gives answers in that regard—at least from a mathematical standpoint—by analyzing the interaction of individuals within a group.

The Chatterjee group at ISTA uses game theory to address central questions in computer science. Their newest framework, published in PNAS, now details how certain structures of neighboring individuals can boost cooperation throughout a system.

The Prisoner’s Dilemma

Game theory was first presented in “The Theory of Games and Economic Behavior”, published in 1944 by mathematicians and economists Oskar Morgenstern and John von Neumann. Soon after, the Prisoner’s Dilemma turned into the central topic in game theory. “It’s a simple ‘game’ that describes the options we have in many real-world scenarios,” explains Jakub Svoboda, PhD student and first author of the study.

The original mathematical concept involves two prisoners who have the option to betray each other or to cooperate. If they both cooperate, they share a significant reward. When one cooperates and the other player betrays, only the defector gets the benefit. Moreover, the individual benefit would be greater than their share if both cooperated. When both players betray each other, they receive no benefit. The same math not only applies in this scenario but also to an arms race between countries, the lives of bacteria, or even daily situations like deciding who should unload the dishwasher in a shared office kitchen.
From the original framework, it seems like betraying is the most beneficial for individuals. Yet, cooperation is still observed in real-world situations. How come?

“Various mechanisms can foster cooperation,” explains Svoboda. “One of them is reciprocity, which suggests that through certain repeated actions, we might build trust and then cooperate.” An example is seeing your colleague starting the dishwasher every day, leaving your favorite mug clean and ready for your morning coffee. In response, you might begin to help by unloading the dishwasher—a mutual exchange of actions. Another key factor is how individuals are interconnected, essentially the network’s structure. To test these structures, the scientists in the Chatterjee group use spatial games.

Cooperation Tetris

In spatial games, individuals are placed on a grid, interacting based on their spatial relations. They either cooperate or not. While playing a game, individuals might see neighbors doing well. Subsequently, they adopt their strategy. This interconnection influences the spreading of cooperation. Networks (clusters) are formed, effecting the broader dynamics of the whole system. This is very similar to playing Tetris on a Game Boy, where a single block can affect its surroundings and determine the placement of subsequent, ultimately bringing the entire system together.

“It has been known that interconnecting structures like these slightly increase the rate of cooperation,” Svoboda continues. “In our new study, we looked at the potential optimal scenario.” The scientists drew inspiration from natural evolution, where constant selection of structural changes can significantly influence the dynamic of a whole population. For example, Darwin’s finches illustrate how such changes can manifest: They have evolved different beak shapes adapted to various food supplies available on the Galápagos Island.

“We hoped that the role of the structure in spatial games could be similarly strong,” Svoboda says. With their new framework, the scientists discovered structures that could boost cooperation in such spatial games. “Our structures show a surprisingly strong boosting property, the best we’ve ever seen,” he adds. The structures look like a string of stars and require areas with many neighbors to be next to places with only a few neighbors.

How this new model and these network structures can be applied to society is still to be seen. In the next months, Svoboda and the scientists from the Chatterjee group will work on generalizing their results to other games and different settings. Due to the broad applications for spatial games, the new proposed structures, however, could find their way also into biology. For instance, biologists can use the new structures to speed up evolution in so-called “bioreactors”, devices with a controlled environment, used to cultivate microorganisms for research or in industry such as biotechnology or pharmaceuticals.


Funding information
This project was supported by funding from the European Research Council (ERC) CoG 863818 (ForM-SMArt) and the Austrian Science Fund (FWF) 10.55776/COE12.

Original publication:

Jakub Svoboda & Krishnendu Chatterjee. 2024. Amplifiers of Cooperation for Spatial Games. PNAS. DOI: (https://doi.org/10.1073/pnas.2405605121)

More information:

(https://ista.ac.at/en/research/chatterjee-group/)
Research group on Computer-Aided Verification, Game Theory

ImageSource © Zuzana Drázdová
Jakub Svoboda. The fourth-year PhD student uses his mathematical knowledge to delve deep into evolutionary dynamics.