Despite the risk of sleeping with the fishes, prisoners will always choose to be rats — at least, idealized prisoners always do in a classic mathematical scenario meant to explore cooperation and betrayal. But tweaking the scenario to allow successful prisoners to expand their circle of influence causes cooperation to blossom, new research shows.
This new variation of the Prisoner’s Dilemma, perhaps the most famous scenario studied in a branch of mathematics called game theory, helps illuminate when and how the players in the game will choose cooperation over betrayal. Previous research has shown that the web of connections among prisoners can lead to cooperation, but this study is the first that allows that web of connections to evolve over time, simulating the ability of successful prisoners to, essentially, win friends and influence people.
Cooperation always grew to become the dominant strategy whenever the sphere of influence of any one player was limited to a medium-sized “Goldilocks Zone” of about 50 players. If these social networks were too small or too large, the game would become overrun by betrayal, the researchers report online and in an upcoming issue of Europhysics Letters.
“The question that we wanted to answer is how can such cooperative networks evolve” starting from a simple, randomized network, says Matjaž Perc, a physicist at the University of Maribor in Slovenia. “We found that by adding this simple process for evolving the network connections, we arrived at, not the same graph, but a very similar graph” to those that promoted cooperation in previous research.