Many economic situations involve the division of bads. We study a noncooperative game model for this type of division problem. The game resembles a standard multilateral bargaining model, but in our case, perpetual disagreement is not a feasible outcome. The driving feature of the model is that a player that makes an unacceptable proposal (causing breakdown with some probability) is made to internalize all the costs in case of breakdown. We show that as the probability of exogenous breakdown goes to zero, this game implements some competitive divisions in Markov perfect equilibria: the limit of any convergent sequence of equilibrium outcomes is a competitive division, but a competitive division may not be a limit of the equilibrium outcomes.

许多经济情况涉及利害关系的划分。我们针对这种划分问题研究了一种非合作博弈模型。博弈类似于标准的多边谈判模型，但在我们的案例中，永久性的分歧不是可行的结果。该模型的驱动特征是提出了提出不可接受的建议（有可能导致故障）的参与者将发生故障时的所有成本内部化。我们证明，随着外生崩溃的可能性变为零，该博弈在马尔可夫完美均衡中实现了一些竞争性划分：均衡结果的任何收敛序列的极限是竞争性划分，但是竞争性划分可能不是均衡的极限结果。