We present a game in which n persons split a cake, where a distinction between conditional and unconditional offers is made. This distinction sheds light on the contrasting results obtained in the previous literature of multilateral bargaining. By allowing the proposer to make unconditional offers, we show that the game has a unique subgame perfect Nash equilibrium outcome, which coincides with the unique stationary equilibrium outcome of Shaked's unanimity game.
Uniqueness still results when the proposer is selected randomly.
An extension to coalitional bargaining is also discussed.