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Stability and robustness analysis of cooperation cycles driven by destructive agents in finite populations

Rubén J. Requejo1, Juan Camacho1, José A. Cuesta2,3, and Alex Arenas4

  • 1Department de Física, Universitat Autónoma de Barcelona, 08193 Bellaterra, Barcelona, Spain
  • 2Grupo Interdiciplinar de Sistemas Complejos (GISC), Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés, Madrid, Spain
  • 3Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), Universidad de Zaragoza, Campus Río Ebro, 50018 Zaragoza, Spain
  • 4Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain

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Phys. Rev. E 86, 026105 – Published 9 August, 2012

DOI: https://doi.org/10.1103/PhysRevE.86.026105

Abstract

The emergence and promotion of cooperation are two of the main issues in evolutionary game theory, as cooperation is amenable to exploitation by defectors, which take advantage of cooperative individuals at no cost, dooming them to extinction. It has been recently shown that the existence of purely destructive agents (termed jokers) acting on the common enterprises (public goods games) can induce stable limit cycles among cooperation, defection, and destruction when infinite populations are considered. These cycles allow for time lapses in which cooperators represent a relevant fraction of the population, providing a mechanism for the emergence of cooperative states in nature and human societies. Here we study analytically and through agent-based simulations the dynamics generated by jokers in finite populations for several selection rules. Cycles appear in all cases studied, thus showing that the joker dynamics generically yields a robust cyclic behavior not restricted to infinite populations. We also compute the average time in which the population consists mostly of just one strategy and compare the results with numerical simulations.

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Phys. Rev. E 86, 026105– Published 9 August, 2012
  • Received 19 March 2012

©2012 American Physical Society

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