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Public Goods With Punishment and Abstaining in Finite and Infinite Populations

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Abstract

The evolution and maintenance of cooperation in human and animal societies challenge various disciplines ranging from evolutionary biology to anthropology, social sciences, and economics. In social interactions, cooperators increase the welfare of the group at some cost to themselves whereas defectors attempt to free ride and neither provide benefits nor incur costs. The problem of cooperation becomes even more pronounced when increasing the number of interacting individuals. Punishment and voluntary participation have been identified as possible factors to support cooperation and prevent cheating. Typically, punishment behavior is unable to gain a foothold in a population, while volunteering alone can efficiently prevent deadlocks in states of mutual defection but is unable to stabilize cooperation. The combined effects of the two mechanisms have surprisingly different consequences in finite and infinite populations. Here we provide a detailed comparison of the two scenarios and demonstrate that driven by the inherent stochasticity of finite populations, the possibility to abstain from social interactions plays a pivotal role, which paves the way for the establishment of cooperation and punishment.

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Authors and Affiliations

  1. Program for Evolutionary Dynamics Department of Organismic and Evolutionary Biology and Department of Mathematics, Harvard University, Cambridge, MA, USA

    Christoph Hauert, Arne Traulsen & Martin A. Nowak

  2. Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada

    Christoph Hauert

  3. Max-Planck-Institute for Evolutionary Biology, Plön, Germany

    Arne Traulsen

  4. Department of Finance, Vienna University of Economics and Business Administration, Vienna, Austria

    Hannelore De Silva née Brandt

  5. Faculty of Mathematics, University of Vienna, Vienna, Austria

    Karl Sigmund

  6. International Institute for Applied Systems Analysis, Laxenburg, Austria

    Karl Sigmund

Authors
  1. Christoph Hauert
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  2. Arne Traulsen
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  3. Hannelore De Silva née Brandt
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  4. Martin A. Nowak
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  5. Karl Sigmund
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Correspondence to Christoph Hauert.

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Hauert, C., Traulsen, A., De Silva née Brandt, H. et al. Public Goods With Punishment and Abstaining in Finite and Infinite Populations. Biol Theory 3, 114–122 (2008). https://doi.org/10.1162/biot.2008.3.2.114

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  • DOI: https://doi.org/10.1162/biot.2008.3.2.114

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