Abstract
The spatial Prisoner’s Dilemma is divided into two stages: strategy selection and action (cooperation/defection) selection. This renewal allows a spatiotemporal strategy that determines the player’s next action based not only on the adversary’s history of actions (temporal strategy) but also on neighbors’ configuration of actions. Several space-time parallelisms and dualisms would hold in this spatiotemporal generalization of strategy. Among them, this note focuses on the generosity (how many defections are tolerated). A temporal strategy involving temporal generosity, such as Tit for Tat (TFT), exhibited good performance such as noise tolerance. We report that a spatial strategy with spatial generosity can maintain a cluster of cooperators by forming a membrane that protects against defectors. The condition of membrane formation can be formulated with the spatial generosity exceeding a certain threshold determined by the number of neighborhoods.
This is a preview of subscription content, log in via an institution to check access.
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
Axelrod, R.: The Evolution of Cooperation. Basic Books, New York (1984)
Nowak, M.A., May, R.M.: Evolutionary games and spatial chaos. Nature 359, 826–829 (1992)
Wolfram, S.: A New Kind of Science. Wolfram Media, 437–440 (2002)
Hauert, C., Doebeli, M.: Spatial structure often inhibits the evolution of cooperation in the spatial Snowdrift game. Nature 428, 643–646 (2004)
McNamara, J.M., Barta, Z., Houston, A.I.: Variation in behaviour promotes cooperation in the Prisoner’s Dilemma game. Nature 428, 745–748 (2004)
Szabó, G., Hauert, C.: Phase Transitions and Volunteering in Spatial Public Goods Games. Phys. Rev. Lett. 89, 118101 (2002)
Ishida, Y., Tokumitsu, M.: Asymmetric Interactions between Cooperators and Defectors for Controlling Self-Repairing. LNCS (LNAI), vol. 5179 (2008)
Ohtsuki, H., Hauert, C., Lieberman, E., Nowak, M.A.: A simple rule for evolution of cooperation on graphs and social networks. Nature 441, 502–505 (2006)
dos Santos Soares, R.O., Martinez, A.S.: The geometrical patterns of cooperation evolution in the spatial prisoner’s dilemma: An intra-group model Physica A: Statistical Mechanics and its Applications, vol. 369, pp. 823–829 (2006)
Szabó, G., Antal, T., Szabó, P., Droz, M.: On the Role of External Constraints in a Spatially Extended Evolutionary Prisoner’s Dilemma Game. In: Garrido, P.L., Marro, J. (eds.) Proceedings of Modeling Complex Systems, AIP Conference, vol. 574, pp. 38–55 (2001)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ishida, Y., Katsumata, Y. (2008). A Note on Space-Time Interplay through Generosity in a Membrane Formation with Spatial Prisoner’s Dilemma. In: Lovrek, I., Howlett, R.J., Jain, L.C. (eds) Knowledge-Based Intelligent Information and Engineering Systems. KES 2008. Lecture Notes in Computer Science(), vol 5179. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85567-5_56
Download citation
DOI: https://doi.org/10.1007/978-3-540-85567-5_56
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85566-8
Online ISBN: 978-3-540-85567-5
eBook Packages: Computer ScienceComputer Science (R0)