Outsiders' threat and consecutive offers

We study the effects of outsiders' threat and consecutive offers in the two-person bargaining model of Shaked and Sutton (1984). In our first model, there are no outsiders and the firm can make two consecutive offers for every given number of periods. Our first model has the same unique equilibrium as in Shaked and Sutton (1984). In our second model, the firm can switch between rival partners but cannot change the alternating proposing sequence. Our second model has the same perfect equilibrium as in Rubinstein (1982). So the key factor that leads to the equilibrium of Shaked and Sutton (1984) is the possibility of firm's consecutive offers, not the outsiders' threat.