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

Mingming LENG, Mahmut PARLAR

Research output: Journal PublicationsJournal Article (refereed)

19 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)667-672
Number of pages6
JournalNaval Research Logistics (NRL)
Volume57
Issue number7
DOIs
Publication statusPublished - 1 Oct 2010

Fingerprint

Nucleolus
Cooperative Game
Analytic Solution
Characteristic Function
Algebraic Methods
Coalitions
Value Function
Closed-form
Calculate
Cooperative game
Form
Characteristic function

Keywords

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

Cite this

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

In: Naval Research Logistics (NRL), Vol. 57, No. 7, 01.10.2010, p. 667-672.

Research output: Journal PublicationsJournal Article (refereed)

TY - JOUR

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AU - LENG, Mingming

AU - PARLAR, Mahmut

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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

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