### 抄録

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).

元の言語 | English |
---|---|

ページ（範囲） | 227-236 |

ページ数 | 10 |

ジャーナル | International Journal of Game Theory |

巻 | 20 |

発行部数 | 3 |

DOI | |

出版物ステータス | Published - 1992 9 |

外部発表 | Yes |

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### ASJC Scopus subject areas

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

### これを引用

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

研究成果: Article

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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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UR - http://www.scopus.com/inward/citedby.url?scp=34249833755&partnerID=8YFLogxK

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 -