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Phys Rev Lett. 2002 Sep 9;89(11):118101. Epub 2002 Aug 23.

Phase transitions and volunteering in spatial public goods games.

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Research Institute for Technical Physics and Materials Science, P.O. Box 49, H-1525 Budapest, Hungary.


We present a simple yet effective mechanism promoting cooperation under full anonymity by allowing for voluntary participation in public goods games. This natural extension leads to "rock-scissors-paper"-type cyclic dominance of the three strategies, cooperate, defect, and loner. In spatial settings with players arranged on a regular lattice, this results in interesting dynamical properties and intriguing spatiotemporal patterns. In particular, variations of the value of the public good leads to transitions between one-, two-, and three-strategy states which either are in the class of directed percolation or show interesting analogies to Ising-type models. Although volunteering is incapable of stabilizing cooperation, it efficiently prevents successful spreading of selfish behavior.

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