On Competition for Spatially Distributed Resources on Networks

We study the dynamics of the exploitation of a natural resource, distributed in space and mobile, where spatial diversification is introduced by a network structure. Players are assigned to different nodes by a regulator, after he/she decides at which nodes natural reserves are established. The game solution shows how the dynamics of spatial distribution depends on the productivity of the various sites, on the structure of the connections between the various locations, and on the preferences of the agents. At the same time, the best locations to host a nature reserve are identified in terms of the parameters of the model, and it turns out they correspond to the most central (in the sense of eigenvector centrality) nodes of a suitably redefined network which takes into account the nodes productivities.