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On the Structure of Informationally Robust Optimal Mechanisms

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  • Benjamin Brooks
  • Songzi Du

Abstract

We study the design of optimal mechanisms when the designer is uncertain both about the form of information held by the agents and also about which equilibrium will be played. The guarantee of a mechanism is its worst performance across all information structures and equilibria. The potential of an information structure is its best performance across all mechanisms and equilibria. We formulate a pair of linear programs, one of which is a lower bound on the maximum guarantee across all mechanisms, and the other of which is an upper bound on the minimum potential across all information structures. In applications to public expenditure, bilateral trade, and optimal auctions, we use the bounding programs to characterize guarantee‐maximizing mechanisms and potential‐minimizing information structures and show that the max guarantee is equal to the min potential.

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  • Benjamin Brooks & Songzi Du, 2024. "On the Structure of Informationally Robust Optimal Mechanisms," Econometrica, Econometric Society, vol. 92(5), pages 1391-1438, September.
    • Handle: RePEc:wly:emetrp:v:92:y:2024:i:5:p:1391-1438
    DOI: 10.3982/ECTA20240
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    References listed on IDEAS

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    1. Bergemann, Dirk & Brooks, Benjamin & Morris, Stephen, 2020. "Countering the winner's curse: optimal auction design in a common value model," Theoretical Economics, Econometric Society, vol. 15(4), November.
    2. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2016. "Informationally Robust Optimal Auction Design," Working Papers 084_2016, Princeton University, Department of Economics, Econometric Research Program..
    3. Werner Güth & Martin Hellwig, 1986. "The private supply of a public good," Journal of Economics, Springer, vol. 5(1), pages 121-159, December.
    4. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    5. Chen, Yi-Chun & Li, Jiangtao, 2018. "Revisiting the foundations of dominant-strategy mechanisms," Journal of Economic Theory, Elsevier, vol. 178(C), pages 294-317.
    6. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    7. Cremer, Jacques & McLean, Richard P, 1988. "Full Extraction of the Surplus in Bayesian and Dominant Strategy Auctions," Econometrica, Econometric Society, vol. 56(6), pages 1247-1257, November.
    8. He, Wei & Li, Jiangtao, 2022. "Correlation-robust auction design," Journal of Economic Theory, Elsevier, vol. 200(C).
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    Cited by:

    1. Daeyoung Jeong & Tongseok Lim & Euncheol Shin, 2024. "Robust Intervention in Networks," Papers 2501.00235, arXiv.org, revised Feb 2025.
    2. Guanyi Wang, 2024. "Robust Network Targeting with Multiple Nash Equilibria," Papers 2410.20860, arXiv.org, revised Nov 2024.

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