  Heterogeneity has been studied as one of the most common explanations of the
puzzle of cooperation in social dilemmas. A large number of papers have been
published discussing the effects of increasing heterogeneity in structured
populations of agents, where it has been established that heterogeneity may
favour cooperative behaviour if it supports agents to locally coordinate their
strategies. In this paper, assuming an existing model of a heterogeneous
weighted network, we aim to further this analysis by exploring the relationship
(if any) between heterogeneity and cooperation. We adopt a weighted network
which is fully populated by agents playing both the Prisoner's Dilemma or the
Optional Prisoner's Dilemma games with coevolutionary rules, i.e., not only the
strategies but also the link weights evolve over time. Surprisingly, results
show that the heterogeneity of link weights (states) on their own does not
always promote cooperation; rather cooperation is actually favoured by the
increase in the number of overlapping states and not by the heterogeneity
itself. We believe that these results can guide further research towards a more
accurate analysis of the role of heterogeneity in social dilemmas.
