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

Mingming LENG, Mahmut PARLAR

Research output: Journal PublicationsJournal Article (refereed)peer-review

28 Citations (Scopus)


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)
Issue number7
Publication statusPublished - 1 Oct 2010

Bibliographical note

For this project both authors were supported by the General Research Fund of the Hong Kong Research Grants Council under Research Project No. LU340409, and the second author (Mahmut Parlar) was supported by the Natural Sciences and Engineering Research Council of Canada.


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


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