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Symmetric Equilibria in Spatially Distributed Extraction Games with Nonlinear Growth

Author

Listed:
  • Filippo de Feo

    (TUB - Technical University of Berlin / Technische Universität Berlin)

  • Giorgio Fabbri

    (GAEL - Laboratoire d'Economie Appliquée de Grenoble - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes, CNRS - Centre National de la Recherche Scientifique)

  • Silvia Faggian

    (Université de Venise Ca’ Foscari | Università Ca’ Foscari di Venezia)

  • Giuseppe Freni

    (PARTHENOPE - Università degli Studi di Napoli “Parthenope” = University of Naples)

Abstract

We study optimal and strategic extraction of a renewable resource that is distributed over a network, migrates mass-conservingly across nodes, and evolves under nonlinear (concave) growth. A subset of nodes hosts extractors while the remaining nodes serve as reserves. We analyze a centralized planner and a noncooperative game with stationary Markov strategies. The migration operator transports shadow values along the network so that Perron-Frobenius geometry governs long-run spatial allocations, while nonlinear growth couples aggregate biomass with its spatial distribution and bounds global dynamics. For three canonical growth families, logistic, power, and log-type saturating laws, under related unilities, we derive closed-form value functions and feedback rules for the planner and construct a symmetric Markov equilibrium on strongly connected networks. To our knowledge, this is the first paper to obtain explicit policies for spatial resource extraction with nonlinear growth and, a fortiori, closed-form Markov equilibria, on general networks.

Suggested Citation

  • Filippo de Feo & Giorgio Fabbri & Silvia Faggian & Giuseppe Freni, 2025. "Symmetric Equilibria in Spatially Distributed Extraction Games with Nonlinear Growth," Working Papers hal-05395762, HAL.
    • Handle: RePEc:hal:wpaper:hal-05395762
    Note: View the original document on HAL open archive server: https://hal.science/hal-05395762v1
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