  This paper proposes a strategic model of pollution control. A firm,
representative of the productive sector of a country, aims at maximizing its
profits by expanding its production. Assuming that the output of production is
proportional to the level of pollutants' emissions, the firm increases the
level of pollution. The government of the country aims at minimizing the social
costs due to the pollution, and introduces regulatory constraints on the
emissions' level, which then effectively cap the output of production.
Supposing that the firm and the government face both proportional and fixed
costs in order to adopt their policies, we model the previous problem as a
stochastic impulse two-person nonzero-sum game. The state variable of the game
is the level of the output of production which evolves as a general linearly
controlled one-dimensional Ito-diffusion. Following an educated guess, we first
construct a pair of candidate equilibrium policies and of corresponding
equilibrium values, and we then provide a set of sufficient conditions under
which they indeed realize an equilibrium. Our results are complemented by a
numerical study when the (uncontrolled) output of production evolves as a
geometric Brownian motion, and the firm's operating profit and the government's
running cost functions are of power type. An analysis of the dependency of the
equilibrium policies and values on the model parameters yields interesting new
behaviors that we explain as a consequence of the strategic interaction between
the firm and the government.
