A condition for cooperation in a game on complex networks |
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Authors: | Konno Tomohiko |
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Institution: | 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 |
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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. |
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Keywords: | Games Cooperation Prisoner's Dilemma Networks Analytical solution |
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