A \Nash equilibrium in Nash bargains" has become the workhorse bargaining model in applied analyses of bilateral oligopoly. This paper proposes a non-cooperative foundation for \Nash-in-Nash" bargaining that extends the Rubinstein (1982) model to multiple upstream and downstream rms. Assuming there exists gains from trade for each rm pair, we prove that there exists an equilibrium with immediate agreement and negotiated prices that correspond to Rubinstein prices if and only if the marginal contribution of a set of agreements is weakly greater than the sum of the agreements’ marginal contributions. We provide stronger conditions under which equilibrium prices are unique.