Abstract
We study unanimity bargaining on the division of a surplus in the presence of monotonicity constraints. The monotonicity constraints specify a complete order on the players, which has to be respected by the shares in the surplus the players obtain in any bargaining outcome. A player higher in the order should not receive a lower share of the surplus. We analyze the resulting subgame perfect equilibria in stationary strategies and show that they are characterized by the simpler notion of bargaining equilibrium. Bargaining equilibria are shown to be unique and to have the property that players ranked strictly higher obtain strictly higher shares in the surplus. The key question is whether the bargaining advantage of a higher-ranked player persists when the probability of breakdown of bargaining tends to zero. We argue that such is not the case by showing that bargaining equilibria have a unique limit equal to an equal division of the surplus. It then follows that the limit also coincides with the Nash bargaining solution for this problem.
Highlights
The path-breaking paper by Rubinstein (1982) on alternating offers bargaining has spurred an extensive literature to explain the crucial factors that determine the division of a surplus among a group of players
If a team carries out a joint project, it would be customary that the team leader should not be paid less than the other team members
It may well happen at equilibrium that a player accepts a proposal which is very unfavorable to him in the knowledge that it will be rejected by a player that responds. To avoid such inessential multiplicity, we introduce a more basic notion of equilibrium, called bargaining equilibrium, which is shown to be essentially equivalent to the notion of SSPE
Summary
The path-breaking paper by Rubinstein (1982) on alternating offers bargaining has spurred an extensive literature to explain the crucial factors that determine the division of a surplus among a group of players. The literature on multilateral bargaining with unanimous agreement has shown convergence of bargaining equilibrium proposals to the Nash bargaining solution, see Hart and Mas-Colell (1996), Laruelle and Valenciano (2007), Miyakawa (2008), Kultti and Vartiainen (2010), and Britz et al (2010) All these papers need differentiability assumptions with respect. We demonstrate that in the case with an arbitrary number of players and an arbitrary monotonicity constraints, the limit proposal is unique and leads to an equal division of the surplus. 7. Section 8 proves that limit equilibria are unique, lead to an equal division of the surplus, and correspond to the Nash bargaining solution for this problem.
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