Shapley's conjecture on the cores of abstract market games

• 成果类型: Article
• 署名作者: Cao, Zhigang; Qin, Chengzhong; Yang, Xiaoguang
• 署名单位: Beijing Jiaotong University; University of California System; University of California Santa Barbara; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2017.08.006
• 发表日期: 2018
• 页码: 466-477
• 关键词: Assignment games; complements; substitutes; core; Convex games

摘要

Shapley (1955) introduced the model of an abstract market game as a generalization of the assignment game model, among several other models. He conjectured that abstract market games possess non-empty cores. We analyze properties of abstract market games and provide a proof of this conjecture for cases with four or fewer players. We show by example that, in general, the structure of an abstract market game is not strong enough to guarantee the nonemptiness of the core. We establish supplemental conditions for the conjecture to hold. Our supplemental conditions are satisfied by the assignment games and abstract market games with one side consisting of a single player as with package auction games in Ausubei and Milgrom (2002). (C) 2017 Elsevier Inc. All rights reserved.