External Environmental Impact for Evolutionary Prisoner's Games on Lattices

This paper studies the role of external environment in the evolution of cooperation. Due to the bounded rationality of players, external environment of individuals does matters on the evolution. The more the amount of cooperators a player's neighborhood has, expectantly, the more confident the player will be in its current choice. Based on this point, two updating rules on regular lattices are introduced concerning external environmental effects. For the first rule, a focal player's payoff is affected proportionally with the difference between the number of cooperators and that of defectors in its group; in the second case, one's payoff is exponentially effected by that difference in its neighbors. On account of the external influence to central individuals, simulation results show that the external environment exerts a significant positive function on the increasing of cooperation level in populations.