Potential Games in the Economics and Management of Pollution

Onésimo Hernández-Lerma () and Héctor Jasso-Fuentes ()
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Onésimo Hernández-Lerma: Cinvestav, Department of Mathematics
Héctor Jasso-Fuentes: Cinvestav, Department of Mathematics

A chapter in Handbook of Visual, Experimental and Computational Mathematics, 2026, pp 743-759 from Springer

Abstract: Abstract This chapter examines a pollution management model involving N ≥ 2 $$N\geq 2$$ firms that periodically produce a specific product, contributing to environmental pollution within a specific region. At the same time, the local government implements cleanup measures to mitigate this pollution. Each firm aims to maximize its individual payoff in a noncooperative way over time. Meanwhile, the government imposes cleanup costs on the firms but tries to maintain a minimum rate to encourage their continued presence in the region. The model is initially framed as a Nash-Stackelberg game but can be reformulated as a potential game based on its characteristics. Consequently, the focus shifts to identifying a single minimax strategy. To determine this minimax strategy, Pontryagin’s maximum principle and techniques from convex analysis are employed.

Keywords: Pollution models; Nash-Stackelberg equilibria; Potential games; Minimax-equilibria; Pontryagin’s maximum principle (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-16368-4_47

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