Shapley's Conjecture on the Cores of Abstract Market Games

23 Pages Posted: 1 Jun 2017 Last revised: 7 Feb 2018

See all articles by Zhigang Cao

Zhigang Cao

Beijing Jiaotong University - School of Economics and Management

Cheng-Zhong Qin

University of California, Santa Barbara (UCSB) - Department of Economics

Xiaoguang Yang

Chinese Academy of Sciences (CAS)

Date Written: May 29, 2017

Abstract

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 Ausubel and Milgrom (2002).

Keywords: Assignment games,complements,substitutes,core,convex games

JEL Classification: C71,C78

Suggested Citation

Cao, Zhigang and Qin, Cheng-Zhong and Yang, Xiaoguang, Shapley's Conjecture on the Cores of Abstract Market Games (May 29, 2017). Games and Economic Behavior, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2977041 or http://dx.doi.org/10.2139/ssrn.2977041

Zhigang Cao (Contact Author)

Beijing Jiaotong University - School of Economics and Management ( email )

China

Cheng-Zhong Qin

University of California, Santa Barbara (UCSB) - Department of Economics ( email )

2127 North Hall
Santa Barbara, CA 93106
United States

Xiaoguang Yang

Chinese Academy of Sciences (CAS) ( email )

52 Sanlihe Rd.
Datun Road, Anwai
Beijing, Xicheng District 100864
China

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