Protection of Cooperative Clusters by Membrane

  • Yoshiteru IshidaEmail author
Part of the Intelligent Systems Reference Library book series (ISRL, volume 101)


Our spatial Prisoner’s Dilemma is divided into two stages: strategy selection and action (cooperation/defection) selection (named second-order cellular automata). 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 (spatial strategy). Several space-time parallelisms and dualisms would hold in this spatiotemporal generalization of strategy. Among them, this chapter focuses on generosity (how many defections are tolerated). A temporal strategy involving temporal generosity, such as Tit for Tat (TFT), exhibits 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 as the spatial generosity exceeding a certain threshold determined by the number of neighborhoods.


Spatial Prisoner’s Dilemma Spatiotemporal strategy Generosity Second-order cellular automata Membrane formation Protection of cooperative cluster 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Computer ScienceToyohashi University of TechnologyToyohashiJapan

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