• prisoner's dilemma model;
  • public goods game;
  • lattice geometries


The evolution of cooperation among unrelated individuals in human and animal societies remains a challenging issue across disciplines. In this context, two models have attracted most attention: the prisoner's dilemma for pairwise interactions and the public goods game for group interactions. The two games share many features as demonstrated by the close linkage of their cores. In spatially structured systems with individuals arranged on a lattice we investigate effects of group size and lattice geometry on the success of cooperators and defectors in compulsory and voluntary interactions. The geometry (square versus honeycomb), i.e., the connectivity turns out to have surprisingly pronounced and robust effects on the fate of cooperators. Apparently they thrive more easily on honeycomb lattices. As expected, it becomes increasingly difficult to promote cooperation in sizable groups but voluntary participation significantly lowers the threshold for persistent cooperative behavior. In fact, this effect is even more pronounced for larger groups. The risk avoiding option to not participate provides additional protection to clusters of cooperators against exploitation and introduces rock-scissors-paper-type cyclic dominance, which gives rise to intriguing spatio-temporal patterns. © 2003 Wiley Periodicals, Inc.