Sequencing bilateral negotiations with externalities

We study the optimal sequence of bilateral negotiations between one principal and two agents, whereby the agents have different bargaining power. The principal chooses whether to negotiate first with the stronger or the weaker agent. We show that the joint surplus is highest when the principal negotiates with the stronger agent first, independent of externalities between agents being positive or negative. The sequence chosen by the principal maximizes the joint surplus if there are negative externalities. Instead, if externalities are positive, the principal often prefers to negotiate with the weaker agent first. We also demonstrate that the sequence can be non-monotonic in the externalities and provide conditions for simultaneous timing to be optimal.