Title

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

Document Type

Journal article

Source Publication

Naval Research Logistics (NRL)

Publication Date

10-1-2010

Volume

57

Issue

7

First Page

667

Last Page

672

Keywords

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

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.

DOI

10.1002/nav.20429

Print ISSN

0894069X

E-ISSN

15206750

Publisher Statement

Copyright © 2010 Wiley Periodicals, Inc.

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Publisher’s Version

Recommended Citation

Leng, M., & Parlar, M. (2010). Analytic solution for the nucleolus of a three-player cooperative game. Naval Research Logistics (NRL), 57(7), 667-672. doi: 10.1002/nav.20429