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Some Characterizations of Lower Probabilities and Other Monotone Capacities through the Use of Mobius Inversion

Author

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  • Alain Chateauneuf

    () (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, Axe Economie mathématique et jeux - CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique - PSE - Paris School of Economics)

  • Jean-Yves Jaffray

    () (DECISION - LIP6 - Laboratoire d'Informatique de Paris 6 - UPMC - Université Pierre et Marie Curie - Paris 6 - CNRS - Centre National de la Recherche Scientifique)

Abstract

Monotone capacities (on finite sets) of finite or infinite order (lower probabilities) are characterized by properties of their Möbius inverses. A necessary property of probabilities dominating a given capacity is demonstrated through the use of Gale's theorem for the transshipment problem. This property is shown to be also sufficient if and only if the capacity is monotone of infinite order. A characterization of dominating probabilities specific to capacities of order 2 is also proved.

Suggested Citation

  • Alain Chateauneuf & Jean-Yves Jaffray, 2008. "Some Characterizations of Lower Probabilities and Other Monotone Capacities through the Use of Mobius Inversion," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00649208, HAL.
  • Handle: RePEc:hal:cesptp:hal-00649208
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00649208
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    Keywords

    Decision theory;

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