While spatially local interactions are ubiquitous between coevolving species sharing recourses (e.g., plant-insect interactions), their effects on such coevolution processes of strategies involving the share of a resource are still not clearly understood. We construct a two-dimensional spatial model of the coevolution of the proposer and responder species in the ultimatum game (UG), in which a pair of proposer and responder individuals at each site plays the UG. We investigate the effects of the locality of interactions and the intensity of selection on the emergence of fairness between these species. We show that the lower intensity of selection favors fair strategies in general, and there are no significant differences in the evolution of fairness between the cases with local and global interactions when the intensity of selection is low. However, as the intensity of selection becomes higher, the spatially local interactions contribute to the evolution of fairer strategies more than the global interactions, even though fair strategies become more difficult to evolve. This positive effect of spatial interactions is expected to be due to the mutual benefit of fairness for both proposer and responder species in future generations, which brings about a dynamic evolution process of fairness.
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