Optimal Control of Competitive Fisheries: A Picard–Pontryagin Framework With Convergence Guarantees and Sensitivity Analysis

This paper introduces a rigorous optimal control framework for bioeconomic fisheries management modeled as a nonlinear differential game between two competing firms. The importance of this study lies in the fact that it offers a rigorous and computationally reliable framework for the management of competitive fisheries, a field where nonlinear ecological economic interactions make analytical solutions challenging and policy design highly sensitive to parameter uncertainty. In contrast to the previous works, this paper combines Pontryagin’s maximum principle with a Picard-type forward–backward iteration and derives explicit mathematical conditions that ensure geometric convergence to the unique Nash equilibrium trajectory. In addition, the extensive sensitivity analysis points to the intrinsic growth rate, catchability parameters, and pricing structure as the main factors that determine equilibrium harvesting strategies and payoffs. These results demonstrate that robust optimal strategies should essentially harmonize biological dynamics with economic incentives. The suggested Picard–Pontryagin method is the one that directly accomplishes this, thus offering a computationally efficient framework for strategic decision-making in the case of competitive renewable resource exploitation under parameter uncertainty.