The evolution of cooperation in systems of interacting agents is a very debated issue: in particular, the influence of the population structure (described by a network) on the emergence of the cooperation has been widely studied in the last two decades. Several social dilemmas have been considered (Prisoner\'s Dilemma Game, Stag Hunt, Snowdrift) as well as different kinds of networks: regular lattices, random networks, etc. I present a detailed numerical analysis of the impact of different topologies (euclidean, small-world, Erdos-Renyi and scale-free networks) on the behaviour of a population playing the Prisoner\'s Dilemma game. At variance with the studies carried up to date, I analyse the dynamical evolution of both the strategies of the players (cooperation and defection) and their updating rules (unconditional imitation, replicator, and Moran); therefore, the system evolve to naturally select the fittest strategy and update mechanism. The results support two main conclusions. First, the shortcuts introduced in a small-world topology have a dramatic effect on the emergence of cooperation and the competition of rules; and, second, increasing the heterogeneity of the network favours probabilistic updating rules against unconditional imitation leading, as a consequence, to a more cooperative global behaviour.