Public Goods with Punishment and Abstaining in Finite and Infinite Populations

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Public Goods with Punishment and Abstaining in Finite and Infinite Populations

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Title: Public Goods with Punishment and Abstaining in Finite and Infinite Populations
Author: Hauert, Christoph; Traulsen, Arne; Brandt, Hannelore; Nowak, Martin A.; Sigmund, Karl

Note: Order does not necessarily reflect citation order of authors.

Citation: Hauert, Christoph, Arne Traulsen, Hannelore Brandt, Martin A. Nowak, and Karl Sigmund. 2008. Public goods with punishment and abstaining in finite and infinite populations. Biological Theory 3(2): 114–122.
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Abstract: The evolution and maintenance of cooperation in human and animal societies challenges 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.
Published Version: doi:10.1162/biot.2008.3.2.114
Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at
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  • FAS Scholarly Articles [8255]
    Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University

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