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A Note on the Shapley Value for Characteristic Functions on Bipartitions

Author

Listed:
  • Sander Muns

    (Erasmus University Rotterdam, and CPB, The Hague)

Abstract

We consider a cooperative game with a bipartition that indicates which players are participating. This paper provides an analytical solution for the Shapley value when the worth of a coalition only depends on the number of participating coalition players. The computational complexity grows linearly in the number of players, which contrasts with the usual exponential increase. Our result remains true when we introduce (i) randomization of the bipartition, and (ii) randomly draw a characteristic function.

Suggested Citation

  • Sander Muns, 2011. "A Note on the Shapley Value for Characteristic Functions on Bipartitions," Tinbergen Institute Discussion Papers 11-124/2, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20110124
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    File URL: https://papers.tinbergen.nl/11124.pdf
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    More about this item

    Keywords

    Shapley value; computational complexity; bipartition;
    All these keywords.

    JEL classification:

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

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