Gradual learning and the evolution of cooperation in the spatial continuous prisoner´s dilemma

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