Inefficient Markov perfect equilibria in multilateral bargaining

We study a complete-information alternating-offer bargaining game in which one "active" player bargains with each of a number of other "passive" players one at a time. In contrast to most existing models, the order of reaching agreements is endogenously determined, hence the active player can "play off'' some passive players against others by moving back and forth bargaining with the passive players. We show that this model has a finite number of Markov Perfect Equilibria, some of which exhibiting wasteful delays. Moreover, the maximum number of delay periods that can be supported in Markov Perfect Equilibria increases in the order of the square of the number of players. We also show that these results are robust to a relaxing of the Markov requirements and to more general surplus functions.