Characterization and implementation of Nash bargaining solutions with non-convexity

Cheng-Zhong Qin, Guofu Tan, Chi Leung WONG

Research output: Working paperWorking paper series

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.
Original languageEnglish
Number of pages42
DOIs
Publication statusPublished - 12 Sep 2017

Publication series

NameUSC Dornsife Institute for New Economic Thinking (USC-INET) Working Paper
PublisherUSC Dornsife Institute for New Economic Thinking
No.17-30

Keywords

  • Bargaining Problem
  • Non-Convexity
  • Nash Solution
  • Nash Product

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    Qin, C-Z., Tan, G., & WONG, C. L. (2017). Characterization and implementation of Nash bargaining solutions with non-convexity. (USC Dornsife Institute for New Economic Thinking (USC-INET) Working Paper; No. 17-30). https://doi.org/10.2139/ssrn.3052015, https://doi.org/10.2139/ssrn.3038023