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The Converse Envelope Theorem

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  • Ludvig Sinander

Abstract

I prove an envelope theorem with a converse: the envelope formula is equivalent to a first‐order condition. Like Milgrom and Segal's (2002) envelope theorem, my result requires no structure on the choice set. I use the converse envelope theorem to extend to general outcomes and preferences the canonical result in mechanism design that any increasing allocation is implementable, and apply this to selling information.

Suggested Citation

  • Ludvig Sinander, 2022. "The Converse Envelope Theorem," Econometrica, Econometric Society, vol. 90(6), pages 2795-2819, November.
    • Handle: RePEc:wly:emetrp:v:90:y:2022:i:6:p:2795-2819
    DOI: 10.3982/ECTA18119
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    References listed on IDEAS

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    Cited by:

    1. Gregorio Curello & Ludvig Sinander, 2024. "The Comparative Statics of Persuasion," CRC TR 224 Discussion Paper Series crctr224_2024_564, University of Bonn and University of Mannheim, Germany.
    2. Rahman, David M., 2024. "Detecting profitable deviations," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    3. Nicolo Cesa-Bianchi & Roberto Colomboni & Maximilian Kasy, 2023. "Adaptive maximization of social welfare," Papers 2310.09597, arXiv.org, revised Jul 2024.
    4. Mark Whitmeyer, 2022. "Making Information More Valuable," Papers 2210.04418, arXiv.org, revised Jun 2024.
    5. Cesa-Bianchi, Nicol`o & Colomboni, Roberto & Kasy, Maximilian, 2024. "Adaptive Maximization of Social Welfare," OSF Preprints u9xjg_v1, Center for Open Science.
    6. Cesa-Bianchi, Nicol`o & Colomboni, Roberto & Kasy, Maximilian, 2024. "Adaptive Maximization of Social Welfare," SocArXiv bgcjk_v1, Center for Open Science.

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