Characterization and Implementation of Nash Bargaining Solutions with Non-Convexity
42 Pages Posted: 19 Sep 2017
Date Written: September 12, 2017
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: Suggested Citation