Symmetric Equilibria in Spatially Distributed Extraction Games with Nonlinear Growth

Filippo de Feo, Giorgio Fabbri, Silvia Faggian and Giuseppe Freni
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Filippo de Feo: TUB - Technical University of Berlin / Technische Universität Berlin
Silvia Faggian: Université de Venise Ca’ Foscari | Università Ca’ Foscari di Venezia
Giuseppe Freni: PARTHENOPE - Università degli Studi di Napoli “Parthenope” = University of Naples

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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.

Keywords: Harvesting; Spatial models; Differential games; Nature reserves (search for similar items in EconPapers)
Date: 2025-12-03
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Working Paper: Symmetric Equilibria in Spatially Distributed Extraction Games with Nonlinear Growth (2025)
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