This paper investigates the uniqueness of subgame perfect (SP) payoffs in a sequential bargaining game. Players are completely informed and the surplus to be allocated follows a geometric Brownian motion. This bargaining problem has not been analysed exhaustively in a stochastic environment. The aim of this paper is to provide a technique to identify the subgame perfect equilibria, i.e. the timing of the agreement and the SP payoffs at which agreement occurs. Even though the main focus is on the uniqueness of the equilibrium, we investigate other features of the equilibrium, such as the Pareto effciency of the outcome and the relation with the Nash axiomatic approach.
