Sustaining environmental resilience: A Stackelberg game

Halkos, George and Papageorgiou, George (2026): Sustaining environmental resilience: A Stackelberg game.

Abstract

This paper develops a dynamic Stackelberg game between a social planner and a resource-extracting firm to analyze the regulation of renewable resource extraction. The planner, as leader, sets extraction quotas, while the firm, as follower, chooses its extraction effort in response. The model is analyzed under exponential resource growth and compares open-loop (pre-committed) and feedback (state-dependent) equilibrium strategies. We show that open-loop equilibria yield environmentally unstable steady states. Stability can be achieved only under feedback strategies, and only when the follower’s valuation of the resource stock is sufficiently sensitive - a condition met under a quadratic value function. A state-dependent tax is further shown to enhance stability by strengthening the corrective feedback between ecological conditions and extraction incentives. The results highlight the limits of static regulation, underscore the critical role of adaptive, feedback-based policies, and provide a formal argument for precautionary and responsive governance in achieving long-run resource sustainability.

• Item Type: MPRA Paper
• Language: English
• Keywords: Differential games; environmental degradation; exponential growth; logistic growth; sustainable growth; Stackelberg game.
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62 - Existence and Stability Conditions of Equilibrium; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; H - Public Economics > H2 - Taxation, Subsidies, and Revenue > H23 - Externalities ; Redistributive Effects ; Environmental Taxes and Subsidies; H - Public Economics > H3 - Fiscal Policies and Behavior of Economic Agents > H32 - Firm; H - Public Economics > H6 - National Budget, Deficit, and Debt > H62 - Deficit ; Surplus; Q - Agricultural and Natural Resource Economics ; Environmental and Ecological Economics > Q5 - Environmental Economics > Q50 - General; Q - Agricultural and Natural Resource Economics ; Environmental and Ecological Economics > Q5 - Environmental Economics > Q52 - Pollution Control Adoption and Costs ; Distributional Effects ; Employment Effects; Q - Agricultural and Natural Resource Economics ; Environmental and Ecological Economics > Q5 - Environmental Economics > Q53 - Air Pollution ; Water Pollution ; Noise ; Hazardous Waste ; Solid Waste ; Recycling; Q - Agricultural and Natural Resource Economics ; Environmental and Ecological Economics > Q5 - Environmental Economics > Q56 - Environment and Development ; Environment and Trade ; Sustainability ; Environmental Accounts and Accounting ; Environmental Equity ; Population Growth

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