Characterization and Implementation of Nash Bargaining Solutions with Non-Convexity

43 Pages Posted: 17 Oct 2017

See all articles by Cheng-Zhong Qin

Cheng-Zhong Qin

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

Guofu Tan

University of Southern California - Department of Economics

Adam Chi Leung Wong

Lingnan University - Department of Economics

Multiple version iconThere are 2 versions of this paper

Date Written: September 12, 2017

Abstract

We consider bargaining problems with compact star-shaped choice sets arising from a class of economic bargaining environments. Convex or comprehensive (relative to the disagreement point) problems are star-shaped but not conversely. We characterize single-valued solutions satisfying the Nash axioms on the class of compact star-shaped bargaining problems. For the case with two players, we show that there are exactly two solutions with each being a dictatorial (in favor of one player) selection of Nash product maximizers. We provide an extensive form game to implement Nash bargaining solutions. We extend our analysis and results to allow for alternative domains, asymmetries, and more than two players. For the n-player case, Nash solutions are shown to be determined by n-round iterative maximizations of Nash products.

Keywords: Bargaining Problem, Non-Convexity, Nash Solution, Nash Product

JEL Classification: C78, D21, D43

Suggested Citation

Qin, Cheng-Zhong and Tan, Guofu and Wong, Chi Leung, Characterization and Implementation of Nash Bargaining Solutions with Non-Convexity (September 12, 2017). USC-INET Research Paper No. 17-30, Available at SSRN: https://ssrn.com/abstract=3052015 or http://dx.doi.org/10.2139/ssrn.3052015

Cheng-Zhong Qin (Contact Author)

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

2127 North Hall
Santa Barbara, CA 93106
United States

Guofu Tan

University of Southern California - Department of Economics ( email )

3620 South Vermont Ave. Kaprielian (KAP) Hall, 300
Los Angeles, CA 90089
United States
213-740-3520 (Phone)

Chi Leung Wong

Lingnan University - Department of Economics ( email )

8 Castle Peak Road
Lingnan University
Hong Kong
Hong Kong

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