  In this work we study a weak Prisoner\^as Dilemma game in which both
strategies and update rules are subjected to evolutionary pressure.
Interactions among agents are specified by complex topologies, and we consider
both homogeneous and heterogeneous situations. We consider deterministic and
stochastic update rules for the strategies, which in turn may consider single
links or full context when selecting agents to copy from. Our results indicate
that the co-evolutionary process preserves heterogeneous networks as a suitable
framework for the emergence of cooperation. Furthermore, on those networks, the
update rule leading to a larger fraction, which we call replicator dynamics, is
selected during co-evolution. On homogeneous networks we observe that even if
replicator dynamics turns out again to be the selected update rule, the
cooperation level is larger than on a fixed update rule framework. We conclude
that for a variety of topologies, the fact that the dynamics coevolves with the
strategies leads in general to more cooperation in the weak Prisoner's Dilemma
game.
