For bilateral bargaining under complete information in network markets, we show that holdup is eliminated when contracts are atomically settled with smart contracts. Applications include over-the-counter trading networks, purchases requiring third-party financing, and other multi-agent markets in which pairs of agents bargain bilaterally over terms that could potentially affect their outside-option values in negotiations with other firms. Under this protocol, the terms of a contract proposed to any firm can be given a “greenlight” by that firm, which automatically converts those terms into a binding contract if and only if the terms proposed to all other firms are also assigned greenlights and thus likewise converted to contracts. We analyze tree-based networks, including hub-spoke and chain networks. Under mild technical conditions, the unique outcome of any Perfect Bayesian Equilibrium is immediate agreement on socially efficient contracts that generate equal expected gains for every firm.