A dynamic game for fiscal federalism with non-local externalities

We address the questions of the patterns and the efficiency of public intervention in a dynamic game model between public agencies in charge of a non-local externality. We give two examples: pollution spreading between water basins (negative externality), and non-uniform contributions from the elite and from the mass to a cultural background (positive externality). We define two extreme cases, depending on whether or not the receiving end of the externality balances the transmitting end. When both balance, the reactivity of the agency structure is strong and the need for redistribution between them is weak. When they do not balance, the externality is more markedly non-local and redistribution is required to balance the fiscal burden (or product) from pigouvian instruments among all beneficiaries. We show that, with a static rule of redistribution that allows them to compute transfers between them as a function of their own strategies, the decentralized agencies' reactivity is somewhat slowed, but they still react faster and more efficiently than a static central agency.