A condition for cooperation in a game on complex networks.
We study a condition of favoring cooperation in Prisoner's Dilemma game on complex networks. There are two kinds of players: cooperators and defectors. Cooperators pay a benefit b to their neighbors at a cost c, whereas defectors only receive a benefit. The game is a death-birth process with weak selection. Although it has been widely thought that b/c>〈k〉 is a condition of favoring cooperation (Ohtsuki et al., 2006), we find that b/c>〈k(nn)〉 is the condition. We also show that among three representative networks, namely, regular, random, and scale-free, a regular network favors cooperation the most, whereas a scale-free network favors cooperation the least. In an ideal scale-free network, cooperation is never realized. Whether or not the scale-free network and network heterogeneity favor cooperation depends on the details of the game, although it is occasionally believed that these favor cooperation irrespective of the game structure.
The Institute of Industrial Science, The University of Tokyo, and Research Fellow of the Japan Society for the Promotion of Science, Komaba 4-6-1, Meguro, Tokyo 153-8505, Japan. tomo.konno@gmail.com
Tomohiko
T
Konno
D003198:Computer Simulation; D003299:Cooperative Behavior; D005716:Game Theory; D008954:Models, Biological; D009716:Numerical Analysis, Computer-Assisted; D011336:Probability