Decentralized one-to-many Bargaining

Abstract

We study a one-to-many bargaining situation in which one active player seeks to reach an agreement with every passive player on how to share the surplus of a joint project. The order of bargaining is not fixed and the active player decides whom to bargain with in each period. We characterize subgame perfect equilibria satisfying a refinement condition. Our model admits a rich set of equilibria and we identify the upper and lower bounds of each player’s equilibrium payoff. In particular, there is a class of divide-and-conquer equilibria, in which the active player creates an endogenous disparity of bargaining power to her own advantage. We also examine whether two natural ordering protocols often assumed in existing studies can sustain endogenously. The queuing protocol may indeed arise in an equilibrium, but it leads to a highly unequal division of the surplus. In contrast, the rotating protocol yields a plausible equilibrium division, but it is not self-enforcing in generic situations.