Abstract
The evolution of cooperative behaviors of small-world networking agents in a snowdrift game mode is investigated, where two agents (nodes) are connected with probability depending on their spatial Euclidean lattice distance in the power-law form controlled by an exponent α. Extensive numerical simulations indicate that the game dynamics crucially depends on the spatial topological structure of underlying networks with different values of the exponent α. Especially, in the distance-independent case of α=0, the small-world connectivity pattern contributes to an enhancement of cooperation compared with that in regular lattices, even with a high cost-to-benefit ratio r. However, with the increment of α > 0, when r ≥ 0.4, the spatial distance-dependent small-world (SDSW) structure tends to inhibit the evolution of cooperation in the snowdrift game.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior. Princeton University Press, Princeton (1944)
Smith, M.J., Szathmáry, E.: The Major Transitions in Evolution. W. H. Freeman, Oxford (1995)
Duncan Lucc, R., Raiffa, H.: Games and Decisions. Dover, New York (1985)
Maynard Smith, J.: Evolution and the Theory of Games. Cambridge University Press, Cambridge (1982)
Gintis, H.: Game Theory Evolving. Princeton University, Princeton (2000)
Maynard Smith, J., Price, G.: The Logic of Animal Conflict. Nature 246, 15–18 (1973)
Sugden, R.: The Economics of Rights, Co-operation and Welfare. Blackwell, Oxford (1986)
Axelrod, R.: The Evolution of Cooperation. Basic Books, New York (1984)
Doebeli, M., Hauert, C.: Models of Cooperation Based on the Prisoner’s Dilemma and the Snowdrift Game. Ecology Letters 8, 748–766 (2005)
Nowak, M.A., May, R.: Evolutionary Games and Spatial Chaos. Nature 359, 826–829 (1992)
Hauert, C., Doebeli, M.: Spatial Structure often Inhibits the Evolution of Cooperation in the Snowdrift Game. Nature 428, 643–646 (2004)
Hofbauer, J., Sigmund, K.: Evolutionary Games and Population Dynamics. Cambridge University Press, Cambridge (1998)
Sysi-Aho, M., et al.: Spatial Snowdrift Game with Myopic Agents. Eur. Phys. J. B. 44, 129–135 (2005)
Tomassini, M., Luthi, L., Giacobini, M.: Hawks and Doves on Small-world Networks. Phys. Rev. E 73, 016132 (2006)
Kleinberg, J.M.: Navigation in a Small World. Nature 406, 845–847 (2000)
Jespersen, S., Blumen, A.: Small-world Networks: Links with Long-tailed Distribution. Phys. Rev. E 62, 6270–6274 (2000)
Sen, P., Chakrabarti, B.K.: Small-world Phenomena and the Statistics of Linear Polymers. J. Phys. A 34, 7749–7755 (2001)
Sen, P., Banerjee, K., Biswas, T.: Phase Transition in a Network with a Range-dependent Connection Probability. Phys. Rev. E 66, 037102 (2002)
Boccaletti, S., et al.: Complex Networks: Structure and Dynamics. Physics Reports 424, 175–308 (2006)
Newman, M.E.J., Watts, D.J.: Scaling and Percolation in the Small-world Network Model. Phys. Rev. E 60, 7332–7342 (1999)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Shang, L. (2008). Cooperative Dynamics in Spatially Structured Populations. In: Huang, DS., Wunsch, D.C., Levine, D.S., Jo, KH. (eds) Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence. ICIC 2008. Lecture Notes in Computer Science(), vol 5227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85984-0_27
Download citation
DOI: https://doi.org/10.1007/978-3-540-85984-0_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85983-3
Online ISBN: 978-3-540-85984-0
eBook Packages: Computer ScienceComputer Science (R0)