Embedding Games with Strategic Complements into Games with Strategic Substitutes

20 Pages Posted: 16 Oct 2015 Last revised: 5 Aug 2018

See all articles by Zhigang Cao

Zhigang Cao

Beijing Jiaotong University - School of Economics and Management

Xujin Chen

Chinese Academy of Sciences (CAS) - Academy of Mathematics and Systems Sciences

Cheng-Zhong Qin

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

Changjun Wang

Beijing University of Technology

Xiaoguang Yang

Chinese Academy of Sciences (CAS)

Date Written: August 1, 2018

Abstract

Games with strategic substitutes (GSS) are generally less tractable than games with strategic complements (GSC). This paper revisits the GSC versus GSS comparison by establishing a novel connection between them. We show through a network perspective that, when the strategy set of each player is the product of some linearly ordered sets that are order isomorphic to subsets of the real space, every GSC can be embedded into a GSS, such that the set of pure strategy Nash equilibria of the former is a projection of that of the latter. In comparison, no GSS with multiple pure strategy Nash equilibria can be embedded into any GSC. In this sense, the class of GSS is broader than the class of GSC.

Keywords: Strategic complements; Strategic substitutes; Supermodular Games; Submodular games; Network games

JEL Classification: C72

Suggested Citation

Cao, Zhigang and Chen, Xujin and Qin, Cheng-Zhong and Wang, Changjun and Yang, Xiaoguang, Embedding Games with Strategic Complements into Games with Strategic Substitutes (August 1, 2018). Journal of Mathematical Economics, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2675011 or http://dx.doi.org/10.2139/ssrn.2675011

Zhigang Cao

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

China

Xujin Chen

Chinese Academy of Sciences (CAS) - Academy of Mathematics and Systems Sciences ( email )

Zhong-Guan-Cun-Dong-Lu 55, Haidian District
Beijing, 100080, P.R., Beijing 100080
China

Cheng-Zhong Qin

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

2127 North Hall
Santa Barbara, CA 93106
United States

Changjun Wang

Beijing University of Technology ( email )

100 Ping Le Yuan
Chaoyang District
Beijing, Beijing 100020
China

Xiaoguang Yang (Contact Author)

Chinese Academy of Sciences (CAS) ( email )

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

Register to save articles to
your library

Register

Paper statistics

Downloads
81
Abstract Views
676
rank
303,008
PlumX Metrics