Analytic solution for the nucleolus of a three-player cooperative game
Naval Research Logistics (NRL)
John Wiley & Sons, Inc.
Three-player cooperative game in characteristic function form, nucleolus, linear programming
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.
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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