This note proves that the two person Nash bargaining theory with polyhedral bargaining regions needs only an ordered field (which always includes the rational number field) as its scalar field. The existence of the Nash bargaining solution is the main part of this result and the axiomatic characterization can be proved in the standard way with slight modifications. We prove the existence by giving a finite algorithm to calculate the Nash solution for a polyhedral bargaining problem, whose speed is of order Bm(m-1) (m is the number of extreme points and B is determined by the extreme points).
ASJC Scopus subject areas
- Social Sciences (miscellaneous)
- Statistics and Probability
- Mathematics (miscellaneous)
- Economics and Econometrics