Differential games of public investment : markovian best responses in the general case

We define a differential game of public investment with a discontinuous Markovian strategy space. The best response correspondence for the game is well-behaved: a best response exists and uniquely maps almost all profiles of opponents' strategies back to the strategy space. Our chosen strategy space thus makes the differential game well-formed as a static game in Markovian strategies, resolving a long-standing open problem in the literature. We provide a user-friendly necessary and sufficient condition for constructing the best response. Our methods do not require specific functional forms. Our theory has general applications, including to problems of noncooperative control of stock pollutants, harvesting of natural resources, and joint investment problems.