Incomplete contracts in dynamic games

I develop a dynamic model of costly private provision of public goods where agents can also invest in cost-reducing technologies. Despite the n+1 stocks in the model, the analysis is tractable and the (Markov perfect) equilibrium unique. The framework is used to derive optimal incomplete contracts in a dynamic setting. If the agents can contract on provision levels, but not on investments, they invest suboptimally little, particularly if the contract is short-term or close to its expiration date. To encourage sufficient investments, the optimal and equilibrium contract is more ambitious if it is short-lasting, and it is tougher to satisfy close to its expiration date. If renegotiation is possible, such a contract implements the first best. The results have important implications for how to design a climate treaty. -- Dynamic private provision of public goods ; dynamic common-pool problems ; dynamic hold-up problems ; incomplete contracts ; renegotiation design ; climate change and climate agreements