We introduce a new noncooperative multilateral bargaining model for network-restricted environments in which players can bargain only with their neighbors. The main theorem characterizes a condition on network structures for efficient equilibria. If the underlying network is either complete or circular, an efficient stationary subgame perfect equilibrium exists for all discount factors—all the players always try to reach an agreement as soon as practicable, and hence no strategic delay occurs. In any other network, however, an efficient equilibrium is impossible if a discount factor is greater than a certain threshold, as some players strategically delay an agreement. We also provide an example of a Braess-like paradox, in which network improvements decrease social welfare. The e-companion is available at https://doi.org/10.1287/opre.2018.1725 .