Multiple agents managing a harmful species population should either work together to control it or split their duties to eradicate it.

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. In particular, managing harmful species often requires cooperation among multiple agents, such as landowners, agencies, and countries. Each agent may have incentives to contribute less to the treatment, leaving more work for other agents, which may result in inefficient treatment. A central question is, therefore, how should a policymaker allocate treatment duties among the agents? Specifically, should the agents work together in the same area, or should each agent work only in a smaller area designated just for her/him? We consider a dynamic game-theoretic model, where a Nash equilibrium corresponds to a possible set of contributions that the agents could adopt over time. In turn, the allocation by the policymaker determines which of the Nash equilibria could be adopted, which allows us to compare the outcome of various allocations. Our results show that fewer agents can abate the harmful species population faster, but more agents can better control the population to keep its density lower. We prove this result in a general theorem and demonstrate it numerically for two case studies. Therefore, following an outbreak, the better policy would be to split and assign one or a few agents to treat the species in a given location, but if controlling the harmful species population at some low density is needed, the agents should work together in all of the locations.