When Does Compromise Prevent More Pollution? C. Clemons, J. Cossey, M. Ferrara, S. Forcey, T. Norfolk, G. Obeng, D. Ricciardi, and G. Young Introduction The word that economists use for a side effect of production is externality. This seemingly neutral term has earned a negative connotation. Exter- nalities, like side effects in general, are usually unwelcome. The discovery of a natural resource in new abundance is followed by a rapid growth in the industry of extracting it—and an equally rapid rise in pollution of the habitats nearby. There will be a cleanup cost, and it must be paid by those benefitting from the resource. That includes the firm that is polluting and the taxpayers who are happy to purchase the product at the pump or through their furnaces. Two questions are raised. It must be decided when the cost should be paid—as C. Clemons is professor of mathematics at The University of Akron. His email address is cclemons@uakron.edu. J. Cossey is assistant professor of mathematics at The Uni- versity of Akron. His email address is cossey@uakron.edu. M. Ferrara is assistant professor of mathematics at the Uni- versity of Colorado, Denver. His email address is michael. ferrara@ucdenver.edu. S. Forcey is assistant professor of mathematics at The Uni- versity of Akron. His email address is sf34@uakron.edu. T. Norfolk is professor of mathematics at The University of Akron. His email address is norfolk@uakron.edu. G. Obeng is instructor of mathematics at Middle Tennessee State University. His email address is George.Obeng@mtsu. edu. D. Ricciardi has just completed her undergraduate degree in mathematics at The University of Akron. Her email ad- dress is ricciardi@uakron.edu. G. Young is professor of mathematics at The University of Akron. His email address is gwyoung@uakron.edu. DOI: http://dx.doi.org/10.1090/noti893 Figure 1. Treated fracking fluid headed for Black Lick Creek in Indiana County, Pa. Photo by Seamus Murphy/VII, as seen in [4]. prevention or as cure—and who should pay what percentage of each. The regulator’s objective is to find a balance between public safety, economic prosperity, and tax revenues. Using a mathematical model will always fall short when politics and psychology are major factors. Philosophical justification for studying a social problem mathematically is found in demon- strating that a solution exists. This emphasized phrase is the punch line of a joke involving fire and a mathematician with a pitcher of water, but it can also support an argument for action. Main Theorem By compromise, we refer to the mutual deci- sion of government and industry to each pay for some fraction of pollution abatement. In game theory terms, compromise is a mixed equilibrium October 2012 Notices of the AMS 1223