Skip to main content
Article
Analytic solution for the nucleolus of a three-player cooperative game
Naval Research Logistics (NRL)
  • Mingming LENG, Lingnan University
  • Mahmut PARLAR, McMaster University, Canada
Document Type
Journal article
Publication Date
10-1-2010
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
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
Citation Information
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