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 re- sponses. We extend the theory of differential games to deal with payoffs under discontinuous strategies. Our methods work under general functional forms.