We propose an n-person pure bargaining game which generalizes Rubinstein's two-person bargaining game, and show that there exists a unique perfect equilibrium outcome. The solution approaches the n-person Nash solution, as defined by Chae [''The n-person Nash bargaining solution with time preference,'' Econ. Lett. 41 (1993), 21-24] in the time preference framework, as the time lapse between bargaining rounds goes to 0. (C) 1994 Academic Press, Inc.