Cooperative and Non‐Cooperative Solutions in a Dynamic Model of Forest Management

ABSTRACT

This study develops a deterministic finite‐horizon bioeconomic control model linking forest biomass, biodiversity, cumulative harvesting pressure, and disturbance‐motivated expected biodiversity losses. Biodiversity is modeled as a productive state variable that feeds back into biomass growth, while cumulative harvesting pressure records the ecological memory of past extraction. Disturbance risk is introduced through a compound Poisson motivation but enters the solved control systems only through a deterministic expected‐loss term, so the analysis should be interpreted as an expected‐drift benchmark rather than a full stochastic‐control treatment. The model compares three governance regimes: a noncooperative open‐loop Nash benchmark with free terminal states, a cooperative regulator with fixed terminal ecological targets, and a cooperative regulator with free terminal states. Numerical solutions show that the noncooperative benchmark generates stronger biomass decline and higher cumulative harvesting pressure because private harvesters do not internalize biodiversity's contribution to future productivity. Cooperative regimes generate more favorable ecological trajectories and objective‐value outcomes in the calibrated benchmark, with endpoint design shaping terminal adjustments. Local sensitivity analysis, based on regime‐consistent perturbations of the boundary‐value problems, indicates that the noncooperative benchmark is more responsive to cumulative‐pressure damage and expected disturbance losses, while cooperative regimes display smoother or more endpoint‐specific responses. Overall, the results highlight the importance of treating biodiversity as productive ecological capital and of accounting for governance structure and endpoint design in dynamic forest‐management models.