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
Publisher
John Wiley & Sons, Inc.
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.
Access to external full text or publisher's version may require subscription.
Full-text Version
Publisher’s Version
Language
English
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