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Volunteering leads to rock–paper–scissors dynamics in a public goods game


Collective efforts are a trademark of both insect and human societies1. They are achieved through relatedness in the former2 and unknown mechanisms in the latter. The problem of achieving cooperation among non-kin has been described as the ‘tragedy of the commons’, prophesying the inescapable collapse of many human enterprises3,4. In public goods experiments, initial cooperation usually drops quickly to almost zero5. It can be maintained by the opportunity to punish defectors6 or the need to maintain good reputation7. Both schemes require that defectors are identified. Theorists propose that a simple but effective mechanism operates under full anonymity. With optional participation in the public goods game, ‘loners’ (players who do not join the group), defectors and cooperators will coexist through rock–paper–scissors dynamics8,9. Here we show experimentally that volunteering generates these dynamics in public goods games and that manipulating initial conditions can produce each predicted direction. If, by manipulating displayed decisions, it is pretended that defectors have the highest frequency, loners soon become most frequent, as do cooperators after loners and defectors after cooperators. On average, cooperation is perpetuated at a substantial level.

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Figure 1: Decisions in round eight after the staged standstill with one single strategy that was most frequent in the first seven rounds.
Figure 2: The predicted prevalence switch occurred more frequently than the unpredicted prevalence switch during the 50 rounds that followed the seven manipulated start rounds.
Figure 3: Average frequencies of the three strategies over a period of ten rounds after synchronizing the 20 groups as follows.


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We thank students at the universities of Bonn, Kiel and Hamburg for participation; T. Bakker, H. Brendelberger, E. Heinz, K.-P. Sauer and M. Zbinden for support; C. Hauert for calculating parameters; and the Max-Planck-Institute of Meteorology for hospitality.

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Correspondence to Manfred Milinski.

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Semmann, D., Krambeck, HJ. & Milinski, M. Volunteering leads to rock–paper–scissors dynamics in a public goods game. Nature 425, 390–393 (2003).

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