### Abstract

Original language | English |
---|---|

Pages (from-to) | 667-672 |

Number of pages | 6 |

Journal | Naval Research Logistics (NRL) |

Volume | 57 |

Issue number | 7 |

DOIs | |

Publication status | Published - 1 Oct 2010 |

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### Keywords

- Three-player cooperative game in characteristic function form
- linear programming
- nucleolus

### Cite this

*Naval Research Logistics (NRL)*,

*57*(7), 667-672. https://doi.org/10.1002/nav.20429

}

*Naval Research Logistics (NRL)*, vol. 57, no. 7, pp. 667-672. https://doi.org/10.1002/nav.20429

**Analytic solution for the nucleolus of a three-player cooperative game.** / LENG, Mingming; PARLAR, Mahmut.

Research output: Journal Publications › Journal Article (refereed)

TY - JOUR

T1 - Analytic solution for the nucleolus of a three-player cooperative game

AU - LENG, Mingming

AU - PARLAR, Mahmut

PY - 2010/10/1

Y1 - 2010/10/1

N2 - The nucleolus solution for cooperative games in characteristic function form is usually computed numerically by solving a sequence of linear programing (LP) problems, or by solving a single, but very large-scale, LP problem. This article proposes an algebraic method to compute the nucleolus solution analytically (i.e., in closed-form) for a three-player cooperative game in characteristic function form. We first consider cooperative games with empty core and derive a formula to compute the nucleolus solution. Next, we examine cooperative games with nonempty core and calculate the nucleolus solution analytically for five possible cases arising from the relationship among the value functions of different coalitions.

AB - The nucleolus solution for cooperative games in characteristic function form is usually computed numerically by solving a sequence of linear programing (LP) problems, or by solving a single, but very large-scale, LP problem. This article proposes an algebraic method to compute the nucleolus solution analytically (i.e., in closed-form) for a three-player cooperative game in characteristic function form. We first consider cooperative games with empty core and derive a formula to compute the nucleolus solution. Next, we examine cooperative games with nonempty core and calculate the nucleolus solution analytically for five possible cases arising from the relationship among the value functions of different coalitions.

KW - Three-player cooperative game in characteristic function form

KW - linear programming

KW - nucleolus

UR - http://commons.ln.edu.hk/sw_master/161

U2 - 10.1002/nav.20429

DO - 10.1002/nav.20429

M3 - Journal Article (refereed)

VL - 57

SP - 667

EP - 672

JO - Naval Research Logistics

JF - Naval Research Logistics

SN - 0894-069X

IS - 7

ER -