A condition for cooperation in a game on complex networks
J. Theor. Biol., 269 (1):
224--233 (2011)DOI: 10.1016/j.jtbi.2010.10.033
Abstract
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>knn 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.