Inter- and intragenerational renewable resource extraction

The paper develops a differential game in which there are overlapping generations of extractors of a renewable resource. We consider intragenerational as well as intergenerational competition between extractors. An interesting feature of the game, which is novel in differential games, is the asynchronous horizons of the players resulting from overlapping generations. A feedback Nash equilibrium characterizing the extraction rates of the generations is identified. In particular, the value functions and the equilibrium strategies are obtained in closed form. An extension of the model to a stochastic model with random resource stock dynamics is obtained.