Power Brokers: Middlemen in Legislative Bargaining

We consider a model of decentralized bargaining among three parties. Parties meet one-on-one after being randomly matched, and can sell or buy votes to one another. The party with a majority of the votes can decide to implement its preferred policy or extend negotiations to capture additional rents. We provide necessary and sufficient conditions for the existence of an equilibrium in which a party acts as an intermediary, transferring resources and voting rights among parties that wouldn't negotiate directly with one another. These conditions are generic, do not require special frictions, and include `well-behaved' (i.e., single-peaked) preference profiles.