A Stackelberg differential game with overlapping generations for the management of a renewable resource

In this paper we study a differential game, for the extraction activity of a renewable good, in which players are overlapping generations. The framework of overlapping generations allows us to consider intragenerational (players in the same generation) and intergenerational (players in different generations) game equilibria. We consider the case in which players, even if identical, face competition in an asymmetric way. Since we consider overlapping generations, players have asynchronous time horizons, in contrast with a number of studies in intertemporal exploitation of resources in which players have identical time horizons. We conclude by considering the case in which players compete in a leader-follower way. We introduce a Stackelberg differential game with asynchronous time horizons and non fixed role structure. The overlapping generations’ framework results in the presence of two different behaviours, the myopic and the non-myopic behaviour. We present a possible solution for the myopic case.