Multilateral bargaining over the division of losses

Many-player divide-the-dollar (DD) games have been a workhorse in the theoretical and experimental analysis of multilateral bargaining. If we deal with a loss or consider many-player divide-the-penalty (DP) games, the theoretical predictions are not simply those from DD games with the sign flipped. We show that the stationary stage-undominated equilibrium (SSUE) is no longer unique in payoffs. The most “egalitarian” equilibrium among the stationary equilibria is a mirror image of the essentially unique SSUE in the Baron–Ferejohn model. That equilibrium's allocations are sensitive to changes in parameters, while the most “unequal” equilibrium is less affected by such changes. Experimental evidence supports the most unequal equilibrium: Most of the approved proposals under a majority rule involve an extreme allocation of the loss to a few members. Other observations such as no delay, the proposer advantage, and the acceptance rate are also consistent with predictions based on the most unequal equilibrium.