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A new integral for capacities

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Abstract

A new integral for capacities is introduced and characterized. It differs from the Choquet integral on non-convex capacities. The main feature of the new integral is concavity, which might be interpreted as uncertainty aversion. The integral is extended to fuzzy capacities, which assign subjective expected values to random variables (e.g., portfolios) and may assign subjective probability only to a partial set of events. An equivalence between the minimum over sets of additive capacities (not necessarily probability distributions) and the integral w.r.t. fuzzy capacities is demonstrated. The extension to fuzzy capacities enables one to calculate the integral also in cases where the information available is limited to a few events.

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Authors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, Tel Aviv, 69978, Israel

    Ehud Lehrer

  2. INSEAD, Bd. de Constance, 77305, Fontainebleau Cedex, France

    Ehud Lehrer

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  1. Ehud Lehrer
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Correspondence to Ehud Lehrer.

Additional information

I wish to thank Eran Hanany, David Schmeidler, Eilon Solan and especially Yaron Azrieli and the anonymous referee of Economic Theory for their helpful comments.

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Lehrer, E. A new integral for capacities. Econ Theory 39, 157–176 (2009). https://doi.org/10.1007/s00199-007-0302-z

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  • DOI: https://doi.org/10.1007/s00199-007-0302-z

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