### Abstract

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).

Original language | English |
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Pages (from-to) | 227-236 |

Number of pages | 10 |

Journal | International Journal of Game Theory |

Volume | 20 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1992 Sep |

Externally published | Yes |

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### ASJC Scopus subject areas

- Social Sciences (miscellaneous)
- Statistics and Probability
- Mathematics (miscellaneous)
- Economics and Econometrics

### Cite this

**The ordered field property and a finite algorithm for the Nash bargaining solution.** / Kaneko, Mamoru.

Research output: Contribution to journal › Article

*International Journal of Game Theory*, vol. 20, no. 3, pp. 227-236. https://doi.org/10.1007/BF01253777

}

TY - JOUR

T1 - The ordered field property and a finite algorithm for the Nash bargaining solution

AU - Kaneko, Mamoru

PY - 1992/9

Y1 - 1992/9

N2 - 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).

AB - 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).

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U2 - 10.1007/BF01253777

DO - 10.1007/BF01253777

M3 - Article

AN - SCOPUS:34249833755

VL - 20

SP - 227

EP - 236

JO - International Journal of Game Theory

JF - International Journal of Game Theory

SN - 0020-7276

IS - 3

ER -