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Sampling methods to estimate the Banzhaf–Owen value

Author

Listed:
  • A. Saavedra-Nieves

    (Universidade de Vigo)

  • M. G. Fiestras-Janeiro

    (Universidade de Vigo)

Abstract

This paper addresses two sampling methods to estimate the Banzhaf–Owen value for general cooperative games. The first approach is based on simple random sampling without replacement of those coalitions that are compatible with the system of unions. Additionally, using the interpretation of the Banzhaf–Owen value as a mean of means, we propose an alternative estimation procedure based on two-stage sampling that reduces the required computation time. Both approaches are analysed by establishing the theoretical statistical properties and bounds of the incurred error and their performance is compared with other sampling methodologies in the literature. Finally, we evaluate these tools on estimating the power of the members of the Board of Governors of the International Monetary Fund (IMF) in 2002 and 2016, and we compare the power of some countries in both compositions.

Suggested Citation

  • A. Saavedra-Nieves & M. G. Fiestras-Janeiro, 2021. "Sampling methods to estimate the Banzhaf–Owen value," Annals of Operations Research, Springer, vol. 301(1), pages 199-223, June.
    • Handle: RePEc:spr:annopr:v:301:y:2021:i:1:d:10.1007_s10479-020-03614-8
    DOI: 10.1007/s10479-020-03614-8
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    References listed on IDEAS

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    Cited by:

    1. A. Saavedra-Nieves, 2023. "On stratified sampling for estimating coalitional values," Annals of Operations Research, Springer, vol. 320(1), pages 325-353, January.

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