On competition for spatially distributed resources on networks

Ranking questions regarding settings where a network of flows connects the resource extraction sites have been central in the network literature, however, they have received scant attention in the metapopulation literature. This study examines the dynamics of the exploitation of a natural resource distributed among and flowing between several nodes connected via a weighted, directed network. The network represents the locations and interactions of the resource nodes. A regulator decides to designate some of the nodes as natural reserves where no exploitation is allowed. The remaining nodes are assigned (one-to-one) to players, who exploit the resource at the node. The present study demonstrates how the equilibrium exploitation and resource stocks depend on the productivity of the resource sites, the structure of the connections between the sites, and the number and preferences of the agents. The best locations to host nature reserves are identified per the model’s parameters and correspond to the most central (in the sense of eigenvector centrality) nodes of a suitably redefined network that considers the nodes’ productivity. The technique proposed in the present study may have applications in decisions regarding the formation of teams when candidate members are heterogeneous in their productivities and connections.