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.
Bibliographical noteFor 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