Multi-agent, multi-site resource allocation under quotas with a Stackelberg leader and network externalities

Xepapadeas, Petros

doi:10.1016/j.econmod.2023.106226

Cited by 3 publications

(1 citation statement)

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“…A more sophisticated numerical method, such as the fitted finite volume method (Nyoumbi & Tambue, 2023), will be necessary to consider the noise-driven resource dynamics. The extension of the proposed mathematical approach to a multisite problem (Xepapadeas, 2023) will also be an interesting future direction, wherein the efficient numerical computation of the associated optimality equation could be a potential challenge. Population dynamics with a delay sometimes arises in applications, and this can also be handled using dynamic programming, although the problem dimension becomes infinite (Benito et al, 2023) in such cases.…”

Section: Discussionmentioning

confidence: 99%

Optimal harvesting policy for biological resources with uncertain heterogeneity for application in fisheries management

Yoshioka

2024

Natural Resource Modeling

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Conventional harvesting problems for natural resources often assume physiological homogeneity of the body length/weight among individuals. However, such assumptions generally are not valid in real‐world problems, where heterogeneity plays an essential role in the planning of biological resource harvesting. Furthermore, it is difficult to observe heterogeneity directly from the available data. This paper presents a novel optimal control framework for the cost‐efficient harvesting of biological resources for application in fisheries management. The heterogeneity is incorporated into the resource dynamics, which is the population dynamics in this case, through a probability density that can be distorted from reality. Subsequently, the distortion, which is the model uncertainty, is penalized through a divergence, leading to a nonstandard dynamic differential game wherein the Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation has a unique nonlinear partial differential term. Here, the existence and uniqueness results of the HJBI equation are presented along with an explicit monotone finite difference method. Finally, the proposed optimal control is applied to a harvesting problem with recreationally, economically, and ecologically important fish species using collected field data.

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Section: Discussionmentioning

confidence: 99%