We study the Markov Perfect Equilibrium in a dynamic game where agents have non-constant time preference, decentralized households determine aggregate savings, and a planner chooses climate policy. The paper is the first to solve this problem with general discounting and general functional forms. With time-inconsistent preferences, a commitment device that allows a planner to choose climate policy for multiple periods is potentially very valuable. Nevertheless, our quantitative results show that while a permanent commitment device would be very valuable, the ability to commit policy for “only” 100 years adds less than two percent to the value of climate policy without commitment. We solve a log-linear version of the model analytically, generating a formula for the optimal carbon tax that includes the formula in Golosov et al. (2014) as a special case. More importantly, we develop new algorithms to solve the general game numerically. Convex damages lead to strategic interactions across generations of planners that lower the optimal carbon tax by forty-five percent relative to the scenario without strategic interactions.