  In recent years, there has been growing interest in the study of
coevolutionary games on networks. Despite much progress, little attention has
been paid to spatially embedded networks, where the underlying geographic
distance, rather than the graph distance, is an important and relevant aspect
of the partner rewiring process. It thus remains largely unclear how individual
partner rewiring range preference, local vs. global, emerges and affects
cooperation. Here we explicitly address this issue using a coevolutionary model
of cooperation and partner rewiring range preference in spatially embedded
social networks. In contrast to local rewiring, global rewiring has no distance
restriction but incurs a one-time cost upon establishing any long range link.
We find that under a wide range of model parameters, global partner switching
preference can coevolve with cooperation. Moreover, the resulting partner
network is highly degree-heterogeneous with small average shortest path length
while maintaining high clustering, thereby possessing small-world properties.
We also discover an optimum availability of reputation information for the
emergence of global cooperators, who form distant partnerships at a cost to
themselves. From the coevolutionary perspective, our work may help explain the
ubiquity of small-world topologies arising alongside cooperation in the real
world.
