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Common mistakes in computing the nucleolus

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  • Guajardo, Mario
  • Jörnsten, Kurt

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 five mistaken examples from this and other journals. 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.

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  • Guajardo, Mario & Jörnsten, Kurt, 2015. "Common mistakes in computing the nucleolus," European Journal of Operational Research, Elsevier, vol. 241(3), pages 931-935.
    • Handle: RePEc:eee:ejores:v:241:y:2015:i:3:p:931-935
    DOI: 10.1016/j.ejor.2014.10.037
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    More about this item

    Keywords

    Game theory; Nucleolus; Cost allocation; Linear programming; Duality;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General

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