  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. 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.
