As shown by Rubinstein (see section 4.4 above), the alternating-move bargaining process between…

As shown by Rubinstein (see section 4.4 above), the alternating-move bargaining process between two players has a unique equilibrium. Shaked has pointed out that with I ≥3 players there are many (subgame-) perfect equilibria (see Herrero 1985 for more details). Prove that with I = 3 players, and for discount factor δ > , any partition of the pie is the outcome of a perfect equilibrium.