The role of topology in the evolution of cooperation

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.