{"ID":2848533,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.25398","arxiv_id":"2510.25398","title":"Centralized and Competitive Extraction for Distributed Renewable Resources with Nonlinear Reproduction","abstract":"We study optimal and strategic extraction of a renewable resource that is distributed over a network, migrates mass-conservatively 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 non-cooperative 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 utilities, 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.","short_abstract":"We study optimal and strategic extraction of a renewable resource that is distributed over a network, migrates mass-conservatively 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 non-cooper...","url_abs":"https://arxiv.org/abs/2510.25398","url_pdf":"https://arxiv.org/pdf/2510.25398v1","authors":"[\"Filippo de Feo\",\"Giorgio Fabbri\",\"Silvia Faggian\",\"Giuseppe Freni\"]","published":"2025-10-29T11:16:43Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}