Pré-Publication, Document De Travail (Working Paper) Année : 2025

Symmetric Equilibria in Spatially Distributed Extraction Games with Nonlinear Growth

Résumé

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.

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hal-05395762 , version 1 (03-12-2025)

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  • HAL Id : hal-05395762 , version 1

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Filippo de Feo, Giorgio Fabbri, Silvia Faggian, Giuseppe Freni. Symmetric Equilibria in Spatially Distributed Extraction Games with Nonlinear Growth. 2025. ⟨hal-05395762⟩
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