A Condition for Cooperation in a Game on Complex Networks

Details A Condition for Cooperation in a Game on Complex Networks A Condition for Cooperation in a Game on Complex Networks

2010-02-27

arxiv.org/abs/1003.0088v4

Journal of Theoretical Biology, 269(1): 224 - 233, 2011

Physics

Physics and Society

Scientific paper

10.1016/j.jtbi.2010.10.033

We study a condition of favoring cooperation in a 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> is a condition of favoring cooperation, we find that b/c> 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.

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