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We characterise the entire set of symmetric stationary Markov-perfect Nash equilibria (MPE) in a class of differential games of public good investment, using the canonical problem of climate change as an example. We provide a sufficient and necessary condition for MPE and show how the set of MPE is constructed. The equilibrium in continuous strategies, unique in our context, is Pareto-dominated by any other equilibrium. We extend the theory of differential games to deal with payoffs under discontinuous strategies. Our methods work under general functional forms.