Cooperation percolation in spatial evolutionary games

Abstract

It has been known that the formation of cooperator clusters plays an important role in spatial evolutionary games. By gathering together, cooperators assist each other and the benefits of mutual cooperation can outweigh the losses against the defector. In this letter, we study the dynamical organization of cooperator clusters in the spatial Stag Hunt game, the Prisoner's Dilemma game and the Snowdrift game. For the above games in square lattices, there exists a continuous phase transition characterized by the emergence of a large spanning cooperator cluster which occurs when the initial fraction of the cooperators exceeds a certain threshold. For games in random graphs, there exist two different kinds of phase transitions. At the first the normalized size of the giant cooperator cluster increases continuously from zero, and at the second the normalized size of the giant cooperator cluster jumps from a low value to a very high value.