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