Gradual learning and the evolution of cooperation in the spatial Continuous Prisoner's Dilemma

摘要

The usual mechanism for modeling learning in spatially structured evolutionary games has todate been imitation of some successful neighbor. However, it seems natural that individuals hesitate toimitate their neighbor's acts, specially if they can imply high costs. Here we study the effect of incorporatingresistance to imitation on these models. Our framework is the spatial Continuous Prisoner's Dilemma. Forthis evolutionary game, it has been reported that occasional errors in the imitation process can explain theemergence of cooperation from a non-cooperative initial state. In this work, we show that this only occursfor particular regimes of low costs of cooperation. Furthermore, we display how resistance gets greaterthe range of scenarios where cooperative individuals can invade selfish populations. In this context, whereresistance to imitation can be interpreted as a general rule of gradual learning, our results show that theless that is learnt in a single step from a successful neighbors, the larger the degree of global cooperationfinally attained. In general, the effect of step-by-step learning can be more efficient for the evolution ofcooperation than a full blast one.