Evolutionary game theory and criticality

We study a regular two-dimensional network of individuals playing the Prisonner's Dilemma game with their neighbors, assigning to each individual the adoption of two different criteria to make a choice between cooperation and defection. For a fraction q < 1 of her time the individual makes her choice by imitating those done by the nearest neighbors, with no payoff consideration. For a fraction epsilon = 1 - q the choice between cooperation and defection of an individual depends on the payoff difference between the most successful neighbor and her payoff. When q = 1 for a special value of the imitation strength K, denoted as K-c, the model of social pressure generates criticality. When q = 0 a large incentive to cheat yields the extinction of cooperation and a modest one leads to the survival of cooperation. We show that for K = K-c the adoption of a very small value of epsilon exerts a bias in favor of either cooperation or defection, as a form of criticality-induced intelligence, which leads the system to select either the cooperation or the defection branch, when K > K-c. Intermediate values of epsilon annihilated criticality-induced cognition and, as consequence, may favor defection choice even in the case when a wise payoff consideration is expected to yield the emergence of cooperation.