A Global Warming Differential Game

Abstract

A differential game of global warming is offered. The game involves individual country social utility functions that balance gains from GHG emissions with damages due to global warming. Two state variables are involved, the concentration of anthropogenic GHG in the atmosphere, and the increase in global temperature, compared to preindustrial times, due to the anthropogenic GHG. Temperature increase adjusts gradually to the effect of increased GHG concentration, while the GHG concentration increases with GHG emissions from countries around the globe, and declines due to the absorptive capacity of the environment, a capacity that is negatively affected by the increased global temperature. A cooperative solution is defined, as is an open-loop equilibrium, and a tax policy is offered that induces an open-loop equilibrium which coincides with the cooperative solution. The tax policy offered serves to bring damages from global warming to all countries into the utility function of each individual country.

Keywords: differential game, global warming, taxation

JEL Classification: C73, H21, Q2