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Universal Choice Spaces and Expected Utility: A Banach-type Functorial Fixed Point

Author

Listed:
  • Stelios Arvanitis

    (Department of Economics, AUEB)

Abstract

This paper utilizes a Banach-type fixed point theorem in a functorial context to develop Universal Choice Spaces for addressing decision problems, focusing on expected utility and preference uncertainty. This generates an infinite sequence of optimal selection problems involving probability measures on utility sets. Each solution at a given stage addresses the preference ambiguity from the previous stage, enabling optimal choices at that level. The Universal Choice Space is characterized as a collection of finite-dimensional vectors of probability distributions, with the mth component being an arbitrary probability measure relevant to the mth stage of the problem. The space is derived as the canonical fixed point of a suitable endofunctor on an enriched category and simultaneously as the colimit of the sequence of iterations of this functor, starting from a suitable object.

Suggested Citation

  • Stelios Arvanitis, 2025. "Universal Choice Spaces and Expected Utility: A Banach-type Functorial Fixed Point," Working Paper 1534, Economics Department, Queen's University.
  • Handle: RePEc:qed:wpaper:1534
    as

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    File URL: https://www.econ.queensu.ca/sites/econ.queensu.ca/files/wpaper/qed_wp_1534.pdf
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    References listed on IDEAS

    as
    1. Efe A. Ok & Nik Weaver, 2023. "Lipschitz Bernoulli Utility Functions," Mathematics of Operations Research, INFORMS, vol. 48(2), pages 728-747, May.
    2. Vassilakis, Spyros, 1992. "Some economic applications of Scott domains," Mathematical Social Sciences, Elsevier, vol. 24(2-3), pages 173-208, November.
    3. MERTENS, Jean-François & ZAMIR, Shmuel, 1985. "Formulation of Bayesian analysis for games with incomplete information," LIDAM Reprints CORE 608, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Heinsalu, Sander, 2014. "Universal type structures with unawareness," Games and Economic Behavior, Elsevier, vol. 83(C), pages 255-266.
    5. Paolo Galeazzi & Johannes Marti, 2023. "Choice Structures in Games," Papers 2304.11575, arXiv.org.
    6. Galeazzi, Paolo & Marti, Johannes, 2023. "Choice structures in games," Games and Economic Behavior, Elsevier, vol. 140(C), pages 431-455.
    7. Lipman, Barton L, 1991. "How to Decide How to Decide How to. . . : Modeling Limited Rationality," Econometrica, Econometric Society, vol. 59(4), pages 1105-1125, July.
    8. Fukuda, Satoshi, 2024. "The existence of universal qualitative belief spaces," Journal of Economic Theory, Elsevier, vol. 216(C).
    9. Rui Gao & Xi Chen & Anton J. Kleywegt, 2024. "Wasserstein Distributionally Robust Optimization and Variation Regularization," Operations Research, INFORMS, vol. 72(3), pages 1177-1191, May.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Expected utility; ambiguity of preferences; infinite regress; enriched category; endofunctor; canonical fixed point; initial algebra; colimit; universal choice space;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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