One-memory in multiperson bargaining

In Rubinstein's (1982) 2-player discounted alternating offers bargaining game, the subgame perfect equilibrium outcome is unique and equivalent to the Nash bargaining solution. However, when there are more than 2 players, every feasible partition can be sustained in subgame perfect equilibrium with a sufficiently high discount factor (Shaked 1986). We prove that when the restriction to one-memory strategies is employed in the multiplayer version of the game, the subgame perfect equilibrium is unique and equivalent to the multiplayer generalization of Rubinstein's. This also implies that the unique subgame perfect equilibrium outcome corresponds to the Nash solution in the multiplayer cooperative game.