Evolution of public cooperation on interdependent networks: The impact of biased utility functions

¹ School of Physics, Nankai University - Tianjin 300071, China
² Department of Physics, Hong Kong Baptist University - Kowloon Tong, Hong Kong
³ Research Institute for Technical Physics and Materials Science - P.O. Box 49, H-1525 Budapest, Hungary, EU
⁴ Faculty of Natural Sciences and Mathematics, University of Maribor - Koroška cesta 160, SI-2000 Maribor, Slovenia, EU

^a szolnoki@mfa.kfki.hu

Received: 22 October 2011
Accepted: 6 January 2012

Abstract

We study the evolution of public cooperation on two interdependent networks that are connected by means of a utility function, which determines to what extent payoffs in one network influence the success of players in the other network. We find that the stronger the bias in the utility function, the higher the level of public cooperation. Yet the benefits of enhanced public cooperation on the two networks are just as biased as the utility functions themselves. While cooperation may thrive on one network, the other may still be plagued by defectors. Nevertheless, the aggregate level of cooperation on both networks is higher than the one attainable on an isolated network. This positive effect of biased utility functions is due to the suppressed feedback of individual success, which leads to a spontaneous separation of characteristic time scales of the evolutionary process on the two interdependent networks. As a result, cooperation is promoted because the aggressive invasion of defectors is more sensitive to the slowing-down than the build-up of collective efforts in sizable groups.