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Can One Hear the Shape of a Decision Problem?

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  • 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.

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  • 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
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    References listed on IDEAS

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    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 Jun 2024.
    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.
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