Punishment Does Not Promote Cooperation Under Exploration Dynamics When Anti-Social Punishment Is Possible

26 Pages Posted: 27 Jul 2013 Last revised: 2 Jul 2014

See all articles by Oliver Hauser

Oliver Hauser

University of Exeter Business School - Department of Economics; Harvard University

Martin Nowak

Harvard University

David G. Rand

Massachusetts Institute of Technology (MIT)

Date Written: April 26, 2014

Abstract

It has been argued that punishment promotes the evolution of cooperation when mutation rates are high (i.e. when agents engage in ‘exploration dynamics’). Mutations maintain a steady supply of agents that punish free-riders, and thus free-riders are at a disadvantage. Recent experiments, however, have demonstrated that free-riders sometimes also pay to punish cooperators. Inspired by these empirical results, theoretical work has explored evolutionary dynamics where mutants are rare, and found that punishment does not promote the evolution of cooperation when this ‘anti-social punishment’ is allowed. Here we extend previous theory by studying the effect of anti-social punishment on the evolution of cooperation across higher mutation rates, and by studying voluntary as well as compulsory Public Goods Games. We find that for intermediate and high mutation rates, adding punishment does not promote cooperation in either compulsory or voluntary public goods games if anti-social punishment is possible: Mutations generate agents that punish cooperators just as frequently as agents that punish defectors, and these two effects cancel each other out. These results raise questions about the effectiveness of punishment for promoting cooperation when mutations are common, and highlight how decisions about which strategies to include in the strategy set can have profound effects on the resulting dynamics.

Keywords: cooperation, anti-social punishment, mutation rates, evolutionary dynamics, exploration dynamics

Suggested Citation

Hauser, Oliver and Nowak, Martin and Rand, David G., Punishment Does Not Promote Cooperation Under Exploration Dynamics When Anti-Social Punishment Is Possible (April 26, 2014). Journal of Theoretical Biology, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2298851 or http://dx.doi.org/10.2139/ssrn.2298851

Oliver Hauser

University of Exeter Business School - Department of Economics ( email )

Streatham Court
Exeter, EX4 4RJ
United Kingdom

HOME PAGE: http://www.oliverhauser.org

Harvard University ( email )

1875 Cambridge Street
Cambridge, MA 02138
United States

HOME PAGE: http://www.hauseroliver.com

Martin Nowak

Harvard University ( email )

1875 Cambridge Street
Cambridge, MA 02138
United States

David G. Rand (Contact Author)

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

HOME PAGE: http://www.daverand.org

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