Multi-person Bargaining With Complementarity: Is There Holdout?

This paper studies a non-cooperative bargaining problem with one buyer and many sellers, focussing on the tension between the complementarity intrinsic to such a setup and efficiency. We address this problem in a very general setup with a technology that allows for variable degrees of complementarity, a bargaining protocol that is symmetric and allows for both secret, as well as publicly observable offers, and strategies that allow for history dependence. We examine equilibria for all parameter values. Interestingly, and in contrast to most of the literature, we demonstrate that there is a large class of parameter values such that an asymptotically efficient equilibrium with a positive buyer payoff exists - thus demonstrating that strategic holdout is not a serious obstacle to the working of the Coase theorem. For robustness we examine alternative contractual forms, i.e. conditional and equity contracts, as well as variations that allow for multiple project implementation and asymmetric sellers.