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A characterization of weighted simple games based on pseudoweightings

Abstract

The paper provides a new characterization of weighted games within the class of simple games. It is based on a stronger form of the point-set-additive pseudoweighting property of simple games. The characterization obtained is of interest in various research fields such as game theory, coherent structures, logic gates, operations research and Boolean algebra. A (monotonic) simple game corresponds to an inequivalent (monotonic) function in Boolean algebra and a weighted game corresponds to a threshold function. The characterization obtained provides a better understanding of these mathematical structures while opening new prospects for solving numerous open problems in these areas.

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Acknowledgements

This research is partially supported by funds from the Spanish Ministry of Science and Innovation Grants MTM2015-66818-P, PID2019-I04987GB-I00. The author wishes to thank two anonymous referees for their helpful comments.

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Correspondence to Josep Freixas.

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Freixas, J. A characterization of weighted simple games based on pseudoweightings. Optim Lett 15, 1371–1383 (2021). https://doi.org/10.1007/s11590-020-01647-3

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Keywords

  • Boolean functions
  • Threshold functions
  • Simple games
  • Weighted games
  • Pseudoweightings
  • Optimization