Phase Transitions and Volunteering in Spatial Public Goods Games

György Szabó, Christoph Hauert

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124 Citations (Scopus)


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.

Original languageEnglish
JournalPhysical review letters
Issue number11
Publication statusPublished - Jan 1 2002


ASJC Scopus subject areas

  • Physics and Astronomy(all)

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