We study a set of bilateral Nash bargaining problems between an upstream input supplier and several differentiated but competing retailers. If The question of how input prices (including wages) are set is subtle. In most retail markets, consumers are atomistic and, thus, reasonably modeled as price takers when patronizing a particular seller. It is less clear who sets the input price in vertically-related markets. In particular, in "tight" oligopolies with a few upstream and a few downstream firms, a framework of bilateral negotiations, with individually-negotiated input prices, seems appropriate. 1 An extensive theoretical literature, both in Industrial Organization and in Labor Economics, has employed Nash axiomatic bargaining to model this setting. IO empirical work often uses structural models that are based on Nash bargaining. It is well known that, in a Nash bargain, the outside option impacts the bargained outcome. The same outside option, however, can be modeled in different ways, depending on the remaining players' behavior in the event of a disagreement. The purpose of this work is to study how the model of the outside option affects the outcome of the negotiation.We make a general methodological point that applies to Nash bargaining in vertically-related markets with downstream competition, when one firm is engaged in multiple negotiations. The simplest setting would involve one upstream firm and two downstream competitors. Indeed, this is the setting analyzed by the seminal work of Horn and Wolinsky (1988, henceforth HW).