In the evolutionary Prisoner's Dilemma, average fitness of a strategy depends on the probability of meeting each other possible strategy.

However, introducing the possibility of correlation radically changes the picture. We now need to compute the average fitness of a strategy given its probability of meeting each other possible strategy. In the evolutionary PD, cooperators whose probability of meeting other cooperators is high do better than defectors whose probability of meeting other defectors is high. Correlation thus favours cooperation.