This chapter examines a pollution management model involving N ≥ 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.