Inter- and intragenerational renewable resource extraction

The paper develops a differential game in which there are overlapping gener ations of extractors of a renewable resource. We consider intragenerational as well as intergenerational competition between extractors. An interestin g feature of the game, which is novel in differential games, is the asynchr onous horizons of the players resulting from overlapping generations. A fee dback Nash equilibrium characterizing the extraction rates of the generatio ns is identified. In particular, the value functions and the equilibrium st rategies are obtained in closed form. An extension of the model to a stocha stic model with random resource stock dynamics is obtained.