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The management of harmful species, including invasive species, pests, parasites, and diseases, is a major, global challenge. Harmful species cause severe damage to ecosystems, biodiversity, agriculture, and human health. The control of harmful species is challenging and often requires cooperation among multiple agents, such as land-owners, agencies, and countries. Agents may have incentives to contribute less, leaving more work for other agents, which can result in inefficient treatment. Here we present a dynamic game theory model and we show that slow treatment may promote a stable solution (Markovian Nash equilibrium) where all agents cooperate to remove the harmful species. The efficiency of this solution depends critically on the life history of the harmful species that determines the speed of optimal treatment. Furthermore, this cooperative equilibrium may coexist with other Nash equilibria, including one dictating no treatment of the harmful species, which implies that coordination among agents is critical for successful control.