When Does Compromise Prevent More Pollution?

We look at a game theoretic scenario in which an industrial firm has the option of voluntarily controlling the pollutants it originates. A regulating agency sets the tax rate on corporate profits as well as a Pigouvian pollution tax: preset percentages of projected cleanup cost which must be covered by the firm. The regulator spends tax revenue to cover the remaining percentage of cleanup costs, and also has the option of subsidizing additional pollution prevention measures. We describe and illustrate the pure and mixed Nash equilibria arising in several variations of the game. We identify situations with multiple simultaneous equilibria, and classify those for which the mixed strategy prevents more pollution than either pure strategy.