Cooperative game for fish harvesting and pollution control

• Published in: Games Vol. 12; no. 3; pp. 1 - 21
• Main Authors: Goudiaby, Mouhamadou Samsidy, Dia, Ben Mansour, Diagne, Mamadou L, Tembine, Hamidou
• Format: Journal Article
• Language: English
• Published: Basel MDPI 2021; MDPI AG
• Subjects: Agricultural cooperatives; Agricultural pollution; Biodiversity; biodiversity preservation; Chemical elements; Climate change; Commercial fishing; cooperative game; Coronaviruses; Costs; Dynamic stability; Economic models; Endangered & extinct species; Eutrophication; Extinction; Farmers; Fertilizers; Fish; Fisheries; Fisheries management; Fishing; Fishing industry; Game theory; Growth models; Harvest; Harvesting; Lakes; Mathematical models; Nonlinear differential equations; optimal control; Optimization; Pandemics; Phosphorus; Pollutants; Pollution control; Population; Renewable resources; Smart cities; Stability analysis; System theory; Taxation; Toxins; Water; Water pollution
• DOI: 10.3390/g12030065
• ISSN: 2073-4336

This paper studies fishery strategies in lakes, seas, and shallow rivers subject to agricultural and industrial pollution. The flowing pollutants are modeled by a nonlinear differential equation in a general manner. The logistic growth model for the fish population is modified to cover the pollution impact on the fish growth rate. We start by presenting the stability analysis of the dynamical system to discern the different types of the evolution of the fish population according to human actions. A cooperative game is formulated to design strategies for preserving the fish population by controlling the pollution as well as the fish stock for harvesting. The sufficient conditions for implementing the cooperative strategy are investigated through an incentive design approach with an adaptive taxation policy for the players. Numerical results are presented to illustrate the benefit of the cooperative for fish population preservation but also for the players' rewards.