Phase Transitions and Volunteering in Spatial Public Goods Games

György Szabó, Christoph Hauert
2002 Physical Review Letters  
Cooperative behavior among unrelated individuals in human and animal societies represents a most intriguing puzzle to scientists in various disciplines. Here 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 i.e. those unwilling to participate in the public enterprise.
more » ... ublic enterprise. In spatial settings with players arranged on a regular lattice this results in interesting dynamical properties and intriguing spatio-temporal patterns. In particular, variations of the value of the public good leads to transitions between one-, two- and three-strategy states which are either 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 and enables cooperators to persist at substantial levels.
doi:10.1103/physrevlett.89.118101 pmid:12225171 fatcat:m2dw4nkaq5hw7pubmym43qp5wm