The paper presents a noncooperative stochastic differential game played by an infinite number of overlapping generations of players. The number and types of players in future generations are uncertain and the state dynamics are given by a stochastic differential equation. A Markovian Nash equilibrium is characterized by a verification theorem of the Harailton-Jacobi-Bellman type. A resource extraction game is offered as an illustration. (C) 2004 Elsevier Ltd. All rights reserved.