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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.25398 |
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| _version_ | 1866917049361498112 |
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| author | de Feo, Filippo Fabbri, Giorgio Faggian, Silvia Freni, Giuseppe |
| author_facet | de Feo, Filippo Fabbri, Giorgio Faggian, Silvia Freni, Giuseppe |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25398 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Centralized and Competitive Extraction for Distributed Renewable Resources with Nonlinear Reproduction de Feo, Filippo Fabbri, Giorgio Faggian, Silvia Freni, Giuseppe Optimization and Control 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. |
| title | Centralized and Competitive Extraction for Distributed Renewable Resources with Nonlinear Reproduction |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2510.25398 |