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Dynamically Eliciting Unobservable Information

Author

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  • Chambers, Christopher P.

    (University of CA, San Diego)

  • Lambert, Nicolas S.

    (Stanford University)

Abstract

We answer the following question: At t = 1, an expert has (probabilistic) information about a random outcome X. In addition, the expert will obtain further information about X as time passes, up to some time t = T + 1 at which X will be publicly revealed. (How) Can a protocol be devised that induces the expert, as a strict best response, to reveal at the outset his prior assessment of both X and the information flows he anticipates and, subsequently, what information he privately receives? (The protocol can provide the expert with payoffs that depend only on the realization of X, as well as any decisions he may take.) We show that this can be done with the following sort of protocol: At the penultimate time t = T, the expert chooses a payoff function from a menu of such functions, where the menu available to him was chosen by him at time t = T - 1 from a menu of such menus, and so forth. We show that any protocol that affirmatively answers our question can be approximated by a protocol of the form described. We show how these results can be extended from discrete time to continuous time problems of this sort.

Suggested Citation

  • Chambers, Christopher P. & Lambert, Nicolas S., 2014. "Dynamically Eliciting Unobservable Information," Research Papers 3036, Stanford University, Graduate School of Business.
    • Handle: RePEc:ecl:stabus:3036
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    Cited by:

    1. Mira Frick & Ryota Iijima & Tomasz Strzalecki, 2019. "Dynamic Random Utility," Econometrica, Econometric Society, vol. 87(6), pages 1941-2002, November.
    2. Bergemann, Dirk & Morris, Stephen & Takahashi, Satoru, 2017. "Interdependent preferences and strategic distinguishability," Journal of Economic Theory, Elsevier, vol. 168(C), pages 329-371.
    3. Karni, Edi & Vierø, Marie-Louise, 2023. "Comparative incompleteness: Measurement, behavioral manifestations and elicitation," Journal of Economic Behavior & Organization, Elsevier, vol. 205(C), pages 423-442.
    4. Edi Karni, 2020. "A mechanism for the elicitation of second-order belief and subjective information structure," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(1), pages 217-232, February.
    5. Frongillo, Rafael M. & Kash, Ian A., 2021. "General truthfulness characterizations via convex analysis," Games and Economic Behavior, Elsevier, vol. 130(C), pages 636-662.

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