Climate change represents a prime example of a negative externality on a global scale. The failure of existing international agreements points out the need for treaties to be self-enforcing. In the language of game theory, this corresponds to a subgame perfect Nash equilibrium in an underlying climate change game. A dynamic game introduced by Dutta and Radner (2004) is used to model the situation. In the basic version, countries only choose emission levels every period, which yield immediate private benefits through their production functions but future global costs by increasing the level of greenhouse gases. Besides a review of the model as well as of existing extensions, my own contributions are threefold: First, I show that certain properties of this dynamic game stem from the fact that there exists an associated repeated game which is strategically equivalent. In particular, equilibrium strategy pro_les are equivalent up to a simple transformation that accounts for the diferent strategy domains in the dynamic and in the repeated game. Furthermore, equilibrium payo_ sets are equivalent up to a linear transformation reecting the exogenously given greenhouse gas level in period zero (which is not accounted for in the repeated game). Second, I investigate numerically how the benchmark outcome, a myopic Markov equilibrium, changes once linearity of the climate change cost function is replaced by convexity. By approximating the value function with Chebyshev polynomials, I find that equilibrium emissions are no longer constant but convex and decreasing in the greenhouse gas level. Third, I introduce trade decisions into the model in order to allow for trade sanctions as punishment device instead of sharp emission increases, which might not be feasible due to short-term irreversibilities. I characterize the best equilibrium under trade sanctions and show under which conditions trade sanctions can achieve a better equilibrium outcome than emission increases.