Von Neumann-Morgenstern solutions in the assignment market

• 成果类型: Article
• 署名作者: Nunez, Marina; Rafels, Caries
• 署名单位: University of Barcelona
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2012.10.002
• 发表日期: 2013
• 页码: 1282-1291
• 关键词: Assignment game; core; Von Neumann-Morgenstern stable set

摘要

The existence of von Neumann-Morgenstern solutions (stable sets) for assignment games has been an unsolved question since Shapley and Shubik (1972) [11]. For each optimal matching between buyers and sellers, Shubik (1984) [12] proposed considering the union of the core of the game and the core of the sub-games that are compatible with this matching. We prove in the present paper that this set is the unique stable set for the assignment game that excludes third-party payments with respect to a fixed optimal matching. Moreover, the stable sets that we characterize, as well as any other stable set of the assignment game, have a lattice structure with respect to the same partial order usually defined on the core. (C) 2013 Elsevier Inc. All rights reserved.