All Symmetric Equilibria in Differential Games with Public Goods

We characterise the entire set of symmetric stationary Markov-perfect Nash equilibria (MPE) in a differential game 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 entire set of MPE is constructed. The equilibrium in continuous strategies, unique in our context, is Pareto-dominated by any other equilibrium. If a Pareto-undominated steady state exists, it is sustained by trigger-like strategies, with deviations above and below the steady state leading to different responses. We extend the theory of differential games to deal with payoffs under discontinuous strategies. Our methods work under general functional forms.