Nash bargaining for log-convex problems

Cheng-Zhong Qin, Shuzhong Shi and Guofu Tan

University of California at Santa Barbara, Recent Works in Economics from Department of Economics, UC Santa Barbara

Abstract: We introduce log-convexity for bargaining problems. With the requirement of some basic regularity conditions, log-convexity is shown to be necessary and sufficient for Nash’s axioms to determine a unique single-valued bargaining solution up to choices of bargaining powers. Specifically, we show that the single-valued (asymmetric) Nash solution is the unique solution under Nash’s axioms without that of symmetry on the class of regular and log-convex bargaining problems, but this is not true on any larger class. We apply our results to bargaining problems arising from duopoly and the theory of the firm. These problems turn out to be log-convex but not convex under familiar conditions. We compare the Nash solution for log-convex bargaining problems with some of its extensions in the literature.

Keywords: Bargaining problem; Non-convexity; Log-convexity; Nash solution; Nash product; Economic Theory; Applied Economics; Econometrics (search for similar items in EconPapers)
Date: 2015-04-01
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Citations: View citations in EconPapers (3)

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Journal Article: Nash bargaining for log-convex problems (2015)
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