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Weighted nucleoli and dually essential coalitions

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  • Tamás Solymosi

    (Corvinus University of Budapest)

Abstract

We consider linearly weighted versions of the least core and the (pre)nuceolus and investigate the reduction possibilities in their computation. We slightly extend some well-known related results and establish their counterparts by using the dual game. Our main results imply, for example, that if the core of the game is not empty, all dually inessential coalitions (which can be weakly minorized by a partition in the dual game) can be ignored when we compute the per-capita least core and the per-capita (pre)nucleolus from the dual game. This could lead to the design of polynomial time algorithms for the per-capita (and other monotone nondecreasingly weighted versions of the) least core and the (pre)nucleolus in specific classes of balanced games with polynomial many dually essential coalitions.

Suggested Citation

  • Tamás Solymosi, 2019. "Weighted nucleoli and dually essential coalitions," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(4), pages 1087-1109, December.
    • Handle: RePEc:spr:jogath:v:48:y:2019:i:4:d:10.1007_s00182-019-00689-x
    DOI: 10.1007/s00182-019-00689-x
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    More about this item

    Keywords

    Per-capita (pre)nucleolus; Least core; Computation;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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