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2760. Symmetric equilibria in spatially distributed extraction games with non linear growth

Invited abstract in session TA-33: Heterogeneity in optimal control problems, stream Optimal Control Theory and Applications.

Tuesday, 8:30-10:00
Room: 42 (building: 303A)

Authors (first author is the speaker)

1. Silvia Faggian
Dip.to di Economia, Università "Ca' Foscari" Venezia
2. Giorgio Fabbri
CNRS Grenoble
3. Giuseppe Freni
Dip. di Studi Economici e Aziendali, Università "Parthenope" Napoli

Abstract

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.
This study extends that in Fabbri et al. (2024) to nonlinear dynamics of the capital stock evolution at the nodes, taking into account evolution equations of logistic or Solow type, establishing the existence of a Markovian equilibrium which is linear in the capital stock and confirming that, consistently with the case of a linear evolution, the equilibrium exploitation and resource stocks depend on the productivity of the resource sites, the structure of the connections between them, 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.

Keywords

Status: accepted

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