Scandinavian Working Papers in Economics

Discussion Papers,
Norwegian School of Economics, Department of Business and Management Science

No 2014/15: Common Mistakes in Computing the Nucleolus

Mario Guajardo () and Kurt Jörnsten ()
Additional contact information
Mario Guajardo: Dept. of Business and Management Science, Norwegian School of Economics, Postal: NHH , Department of Business and Management Science, Helleveien 30, N-5045 Bergen, Norway
Kurt Jörnsten: Dept. of Business and Management Science, Norwegian School of Economics, Postal: NHH , Department of Business and Management Science, Helleveien 30, N-5045 Bergen, Norway

Abstract: Despite linear programming and duality have correctly been incorporated in algorithms to compute the nucleolus, we have found mistakes in how these have been used in a broad range of applications. Overlooking the fact that a linear program can have multiple optimal solutions and neglecting the relevance of duality appear to be crucial sources of mistakes in computing the nucleolus. We discuss these issues and illustrate them in mistaken examples collected from a variety of literature sources. The purpose of this note is to prevent these mistakes propagate longer by clarifying how linear programming and duality can be correctly used for computing the nucleolus.

Keywords: Game theory; Nucleolus; Cost allocation; Linear programming; Duality

JEL-codes: C60; C61; C70

14 pages, April 14, 2014

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