Simultaneous versus sequential offers in dominant player bargaining

We consider bargaining between a number of players that are all essential in creating a surplus. One of the players is dominant in the sense that it ultimately decides whether the surplus will be created. The other players have an incentive to get a large share of the pie for themselves, but leaving enough for the dominant firm that it finds it profitable to create the surplus. Hence, the smaller players have preferences over who they take their share from. When the dominant player makes the first offer in an alternating offer framework, we analyse whether it should conduct negotiations sequentially with some grouping of players, or simultaneously. We demonstrate that the dominant player will prefer simultaneous negotiation. The other players would prefer to negotiate early with the dominant one, and then to see remaining rivals negotiate simultaneously