This research investigates the endogenous choice of centralized or decentralized bargaining and the type of strategic variables by taking into account a vertically-related market where an upstream monopolist bargains with two downstream firms via a two-part input pricing contract. We show that centralized bargaining is the unique equilibrium mode of bargaining, given Cournot or Bertrand competition in the product market, and that choosing the quantity (price) contract is the dominant strategy for both downstream firms under decentralized (centralized) bargaining. When both the type of strategic variables and the mode of bargaining are endogenously determined, the unique equilibrium outcome is choosing price contracts and centralized bargaining, which maximize industry profit, but there is market failure.