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Set-valued capacities: multi-agenda decision making

Author

Listed:
  • Ehud Lehrer

    (Tel Aviv University
    INSEAD)

  • Roee Teper

    (University of Pittsburgh)

Abstract

We study the problem in which a set of agents are required to produce across several different projects (or more generally, agendas), and we consider environments in which resources are constrained and investing (say, time or effort) in one agenda reduces the ability to invest in other agendas. To this end, we introduce a class of capacities we refer to as set-valued: the value of each coalition is a subset of a vector space. For a particular coalition, each vector in its value is associated with a different distribution of the resources invested across the different agendas. In this context, the Choquet and the concave integrals are defined, characterized and shown to be identical if and only if the underlying set-valued capacity is supermodular. We apply the tools developed and introduce a new decision theory.

Suggested Citation

  • Ehud Lehrer & Roee Teper, 2020. "Set-valued capacities: multi-agenda decision making," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(1), pages 233-248, February.
    • Handle: RePEc:spr:joecth:v:69:y:2020:i:1:d:10.1007_s00199-018-1164-2
    DOI: 10.1007/s00199-018-1164-2
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    References listed on IDEAS

    as
    1. Gonzalez, Stéphane & Grabisch, Michel, 2016. "Multicoalitional solutions," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 1-10.
    2. Michel Grabisch, 2016. "Remarkable polyhedra related to set functions, games and capacities," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 301-326, July.
    3. Roee Teper, 2015. "Subjective Independence and Concave Expected Utility," Working Paper 5865, Department of Economics, University of Pittsburgh.
    4. Yaarit Even & Ehud Lehrer, 2014. "Decomposition-integral: unifying Choquet and the concave integrals," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(1), pages 33-58, May.
    5. Michel Grabisch, 2016. "Set Functions, Games and Capacities in Decision Making," Theory and Decision Library C, Springer, number 978-3-319-30690-2, July.
    6. Ehud Lehrer, 2009. "A new integral for capacities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(1), pages 157-176, April.
    7. Lehrer, Ehud & Teper, Roee, 2015. "Subjective independence and concave expected utility," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 33-53.
    8. Roee Teper, 2015. "Subjective Independence and Concave Expected Utility," Working Paper 5866, Department of Economics, University of Pittsburgh.
    9. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
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    Cited by:

    1. Leifan Yan & Tong Kang & Huai Zhang, 2023. "Decomposition Integrals of Set-Valued Functions Based on Fuzzy Measures," Mathematics, MDPI, vol. 11(13), pages 1-14, July.

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    More about this item

    Keywords

    Set-valued capacities; Concave integral; Choquet integral; Supermodular set-valued games;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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