From the bankruptcy problem and its Concede-and-Divide solution to the assignment problem and its Fair Division solution

• 成果类型: Article
• 署名作者: Trudeau, Christian
• 署名单位: University of Windsor
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2017.09.005
• 发表日期: 2018
• 页码: 225-238
• 关键词: Assignment problems; Bankruptcy problems; core; Fair division; Concede-and-divide; Minimal rights

摘要

We revisit two classic problems: the assignment problem, in which matched pairs of agents create value, and the bankruptcy problem, in which we need to share an endowment among agents with conflicting claims. Since Core Selection constrains us to exactly divide the value created by matched agents, the assignment problem corresponds to multiple two-player bankruptcy problems. From this we obtain equivalence between the Concede and-Divide (Aumann and Maschler. 1985) sharing method for the bankruptcy problem and the Fair Division solution (Thompson, 1981) for the assignment problem. In bankruptcy problems, the minimal rights of a claimant is what is left of the endowment when all claimants but himself have received their full claims. By the Minimal Rights First property, it is irrelevant if we distribute the minimal rights first or proceed on the original problem. By adapting the property to the assignment problem, we obtain two characterizations of the Fair Division solution. (C) 2017 Elsevier Inc. All rights reserved.