Analytic solution for the nucleolus of a three‐player cooperative game Journal Articles

abstract

• AbstractThe 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. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010

authors

• Leng, Mingming
• Parlar, Mahmut

status

• published 

publication date

• October 2010

has subject area

• 0102 Applied Mathematics (FoR)
• 0103 Numerical and Computational Mathematics (FoR)
• 1503 Business and Management (FoR)
• Logistics & Transportation (Science Metrix)

published in

• Naval Research Logistics  Journal

keywords

• ALGORITHM
• Operations Research & Management Science
• Science & Technology
• Technology
• linear programming
• nucleolus
• three-player cooperative game in characteristic function form

Digital Object Identifier (DOI)

• 10.1002/nav.20429

start page

• 667

end page

• 672

volume

• 57

issue

• 7