Optimizing multi-stage negotiations

We consider procedures where issues of varying importance and risk are negotiated in stages. Negotiation at any stage requires an agreement at each previous stage. If negotiation terminates, players realize the benefits from all earlier agreements. We formalize this process by a strategic n-stage negotiation game. The expected subgame-perfect equilibrium outcome is characterized by an intuitive, compact formula, which aggregates all the structural elements of the multi-stage process. We describe the optimal negotiation agenda for a given decomposition of the bargaining problem, and we derive intuitive prescriptions for an optimal decomposition.