A noncooperative foundation of the competitive divisions for bads

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.