IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2403.06344.html
   My bibliography  Save this paper

Can One Hear the Shape of a Decision Problem?

Author

Listed:
  • Mark Whitmeyer

Abstract

We explore the connection between an agent's decision problem and her ranking of information structures. We find that a finite amount of ordinal data on the agent's ranking of experiments is enough to identify her (finite) set of undominated actions (up to relabeling and duplication) and the beliefs rendering each such action optimal. An additional smattering of cardinal data, comparing the relative value to the agent of finitely many pairs of experiments, identifies her utility function up to an action-independent payoff.

Suggested Citation

  • Mark Whitmeyer, 2024. "Can One Hear the Shape of a Decision Problem?," Papers 2403.06344, arXiv.org, revised Apr 2024.
    • Handle: RePEc:arx:papers:2403.06344
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2403.06344
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Edward J. Green & Kent Osband, 1991. "A Revealed Preference Theory for Expected Utility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(4), pages 677-695.
    2. Andrew Caplin & Mark Dean, 2015. "Revealed Preference, Rational Inattention, and Costly Information Acquisition," American Economic Review, American Economic Association, vol. 105(7), pages 2183-2203, July.
    3. Jay Lu, 2019. "Bayesian Identification: A Theory for State-Dependent Utilities," American Economic Review, American Economic Association, vol. 109(9), pages 3192-3228, September.
    4. Athey, Susan & Levin, Jonathan, 2018. "The value of information in monotone decision problems," Research in Economics, Elsevier, vol. 72(1), pages 101-116.
    5. de Oliveira, Henrique & Denti, Tommaso & Mihm, Maximilian & Ozbek, Kemal, 2017. "Rationally inattentive preferences and hidden information costs," Theoretical Economics, Econometric Society, vol. 12(2), May.
    6. Dillenberger, David & Lleras, Juan Sebastián & Sadowski, Philipp & Takeoka, Norio, 2014. "A theory of subjective learning," Journal of Economic Theory, Elsevier, vol. 153(C), pages 287-312.
    7. Andrew Caplin & Daniel Martin, 2021. "Comparison of Decisions under Unknown Experiments," Journal of Political Economy, University of Chicago Press, vol. 129(11), pages 3185-3205.
    8. Frongillo, Rafael M. & Kash, Ian A., 2021. "General truthfulness characterizations via convex analysis," Games and Economic Behavior, Elsevier, vol. 130(C), pages 636-662.
    9. Mark Whitmeyer, 2022. "Making Information More Valuable," Papers 2210.04418, arXiv.org, revised Dec 2023.
    10. Michel de Lara & L. Gilotte, 2007. "A tight sufficient condition for Radner-Stiglitz nonconcavity in the value of information," Post-Print hal-00716396, HAL.
    11. Chade, Hector & Schlee, Edward, 2002. "Another Look at the Radner-Stiglitz Nonconcavity in the Value of Information," Journal of Economic Theory, Elsevier, vol. 107(2), pages 421-452, December.
    12. De Lara, Michel & Gilotte, Laurent, 2007. "A tight sufficient condition for Radner-Stiglitz nonconcavity in the value of information," Journal of Economic Theory, Elsevier, vol. 137(1), pages 696-708, November.
    13. Tommaso Denti & Massimo Marinacci & Aldo Rustichini, 2022. "Experimental Cost of Information," American Economic Review, American Economic Association, vol. 112(9), pages 3106-3123, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mark Whitmeyer, 2022. "Making Information More Valuable," Papers 2210.04418, arXiv.org, revised Dec 2023.
    2. Mark Whitmeyer, 2024. "Call the Dentist! A (Con-)Cavity in the Value of Information," Papers 2404.01190, arXiv.org.
    3. Lin, Yi-Hsuan, 2022. "Stochastic choice and rational inattention," Journal of Economic Theory, Elsevier, vol. 202(C).
    4. Daniele Pennesi, 2020. "Identity and information acquisition," Carlo Alberto Notebooks 610, Collegio Carlo Alberto, revised 2021.
    5. Youichiro Higashi & Kazuya Hyogo & Norio Takeoka, 2020. "Costly Subjective Learning," KIER Working Papers 1040, Kyoto University, Institute of Economic Research.
    6. Ellis, Andrew, 2018. "Foundations for optimal inattention," Journal of Economic Theory, Elsevier, vol. 173(C), pages 56-94.
    7. Michel de Lara & Olivier Gossner, 2020. "Payoffs-Beliefs Duality and the Value of Information," Post-Print hal-01941006, HAL.
    8. Peter I. Frazier & Warren B. Powell, 2010. "Paradoxes in Learning and the Marginal Value of Information," Decision Analysis, INFORMS, vol. 7(4), pages 378-403, December.
    9. Ashesh Rambachan, 2022. "Identifying Prediction Mistakes in Observational Data," NBER Chapters, in: Economics of Artificial Intelligence, National Bureau of Economic Research, Inc.
    10. van Staden, Heletjé E. & Boute, Robert N., 2021. "The effect of multi-sensor data on condition-based maintenance policies," European Journal of Operational Research, Elsevier, vol. 290(2), pages 585-600.
    11. Philippe Jehiel & Jakub Steiner, 2020. "Selective Sampling with Information-Storage Constraints [On interim rationality, belief formation and learning in decision problems with bounded memory]," The Economic Journal, Royal Economic Society, vol. 130(630), pages 1753-1781.
    12. Bartosz Maćkowiak & Filip Matějka & Mirko Wiederholt, 2023. "Rational Inattention: A Review," Journal of Economic Literature, American Economic Association, vol. 61(1), pages 226-273, March.
    13. Tommaso Denti & Doron Ravid, 2023. "Robust Predictions in Games with Rational Inattention," Papers 2306.09964, arXiv.org.
    14. Valentino Dardanoni & Paola Manzini & Marco Mariotti & Christopher J. Tyson, 2020. "Inferring Cognitive Heterogeneity From Aggregate Choices," Econometrica, Econometric Society, vol. 88(3), pages 1269-1296, May.
    15. Alexander M. Jakobsen, 2021. "An Axiomatic Model of Persuasion," Econometrica, Econometric Society, vol. 89(5), pages 2081-2116, September.
    16. Hébert, Benjamin & Woodford, Michael, 2023. "Rational inattention when decisions take time," Journal of Economic Theory, Elsevier, vol. 208(C).
    17. Roc Armenter & Michèle Müller-Itten & Zachary Stangebye, 2020. "Rational Inattention via Ignorance Equivalence," Working Papers 20-24, Federal Reserve Bank of Philadelphia.
    18. Mogens Fosgerau & Emerson Melo & André de Palma & Matthew Shum, 2020. "Discrete Choice And Rational Inattention: A General Equivalence Result," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 61(4), pages 1569-1589, November.
    19. Valentino Dardanoni & Paola Manzini & Marco Mariotti & Christopher J. Tyson, 2020. "Inferring Cognitive Heterogeneity From Aggregate Choices," Econometrica, Econometric Society, vol. 88(3), pages 1269-1296, May.
    20. Daniele Pennesi, 2021. "Between Commitment and Flexibility: Revealing Anticipated Regret and Elation," Working papers 071, Department of Economics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2403.06344. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.