Helping your neighbor or focusing on your own tasks? This can be a tough decision, each with its own rewards. Game theory can help us navigate such dilemmas — at least theoretically. Recent research by Jakub Svoboda and Krishnendu Chatterjee from the Institute of Science and Technology Austria (ISTA) unveils new network designs that promote cooperation in a system. These findings may also be applied in biological contexts.
Helping your neighbor or focusing on your own tasks? This can be a tough decision, each with its own rewards. Game theory can help us navigate such dilemmas — at least theoretically. Recent research by Jakub Svoboda and Krishnendu Chatterjee from the Institute of Science and Technology Austria (ISTA) unveils new network designs that promote cooperation in a system. These findings may also be applied in biological contexts.
The topic of cooperation has intrigued researchers for a long time. Understanding the conditions that lead to success among groups of individuals is key, whether in biology, sociology, economics, or political science. Game theory offers insights into this question by examining how group members interact.
The Chatterjee group at ISTA employs game theory to tackle crucial issues in computer science. Their latest framework, recently published in PNAS, elaborates on how certain arrangements among nearby individuals can enhance cooperation throughout a system.
The Prisoner’s Dilemma
Game theory first emerged in “The Theory of Games and Economic Behavior,” released in 1944 by mathematicians and economists Oskar Morgenstern and John von Neumann. Shortly thereafter, the Prisoner’s Dilemma became a fundamental topic within game theory. “It’s a straightforward ‘game’ that illustrates the choices we face in many everyday situations,” explains Jakub Svoboda, a PhD student and the study’s primary author.
This original mathematical model involves two inmates who can either betray one another or work together. If both cooperate, they gain a substantial reward. If one betrays while the other cooperates, the betrayer reaps the benefits. Furthermore, the personal gain from betrayal exceeds what they would receive from mutual cooperation. If both betray, neither receives anything. This mathematical principle applies not just here but also to arms races between nations, bacterial life, or even mundane decisions like who should empty the dishwasher in a communal kitchen.
Initially, it seems that betrayal is the most advantageous choice for individuals. Surprisingly, we still witness cooperation in various real-world scenarios. How is that possible?
“Different mechanisms can encourage cooperation,” notes Svoboda. “Reciprocity is one such mechanism, suggesting that through repeated interactions, we can develop trust and then cooperate.” For instance, if you notice a colleague consistently loading the dishwasher, leaving your favorite mug sparkling clean, you might start helping by unloading it — a mutual exchange of favors. Another important aspect is how individuals are interconnected, essentially the network’s layout. To explore these patterns, the Chatterjee group utilizes spatial games.
Cooperation Tetris
In spatial games, individuals are positioned on a grid and interact based on their proximity. They choose whether to cooperate or not. As people observe their neighbors thriving, they may adopt similar strategies. This interconnection plays a key role in the spread of cooperation. Networks form, impacting the overall dynamics of the system, much like how a single piece in Tetris can influence the surrounding blocks, ultimately guiding the whole structure.
“Previous studies have shown that interconnected structures slightly increase cooperation rates,” Svoboda adds. “In our recent research, we aimed to determine the optimal arrangement.” The researchers were inspired by natural evolution, where consistent selection of structural modifications can greatly alter the dynamics of an entire population. An example is Darwin’s finches, which have developed varied beak shapes suited to distinct food sources available on the Galápagos Islands.
“We anticipated that the role of structure in spatial games could be equally significant,” Svoboda explains. With their newly developed framework, the researchers identified structures that can enhance cooperation within these spatial games. “Our structures showcase an unexpectedly strong cooperative potential, the strongest we’ve observed to date,” he adds. These configurations resemble a string of stars and require areas abundant in neighbors to be adjacent to zones with fewer neighbors.
The application of this new model and its associated network structures in society remains to be determined. In the coming months, Svoboda and the Chatterjee team will work on generalizing their findings to various games and conditions. Given the wide-ranging applications for spatial games, these newly suggested structures may also prove beneficial in biology. For instance, biologists might implement these structures to expedite evolution in so-called “bioreactors,” controlled environments used to cultivate microorganisms for research or applications in biotechnology and pharmaceuticals.
