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Regular type distributions in mechanism design and $$\rho $$ -concavity

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  • Christian Ewerhart

Abstract

Some of the best-known results in mechanism design depend critically on Myerson’s (Math Oper Res 6:58–73, 1981 ) regularity condition. For example, the second-price auction with reserve price is revenue maximizing only if the type distribution is regular. This paper offers two main findings. First, a new interpretation of regularity is developed—similar to that of a monotone hazard rate—in terms of being the next to fail. Second, using expanded concepts of concavity, a tight sufficient condition is obtained for a density to define a regular distribution. New examples of regular distributions are identified. Applications are discussed. Copyright Springer-Verlag 2013

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  • Christian Ewerhart, 2013. "Regular type distributions in mechanism design and $$\rho $$ -concavity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(3), pages 591-603, August.
    • Handle: RePEc:spr:joecth:v:53:y:2013:i:3:p:591-603
    DOI: 10.1007/s00199-012-0705-3
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    Cited by:

    1. Suen, Richard M.H., 2018. "Standard risk aversion and efficient risk sharing," Economics Letters, Elsevier, vol. 173(C), pages 23-26.
    2. Thomas Mariotti & Nikolaus Schweizer & Nora Szech & Jonas von Wangenheim, 2023. "Information Nudges and Self-Control," Management Science, INFORMS, vol. 69(4), pages 2182-2197, April.
    3. Dizdar, Deniz & Moldovanu, Benny & Szech, Nora, 2019. "The feedback effect in two-sided markets with bilateral investments," Journal of Economic Theory, Elsevier, vol. 182(C), pages 106-142.
    4. Schweizer, Nikolaus & Szech, Nora, 2015. "A quantitative version of Myerson regularity," Working Paper Series in Economics 76, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    5. Li, Mengling & Riyanto, Yohanes E. & Xu, Menghan, 2023. "Prioritized organ allocation rules under compatibility constraints," Games and Economic Behavior, Elsevier, vol. 141(C), pages 403-427.
    6. Ryan Cumings-Menon, 2017. "Shape-Constrained Density Estimation via Optimal Transport," Papers 1710.09069, arXiv.org, revised Nov 2018.
    7. Dizdar, Deniz & Moldovanu, Benny & Szech, Nora, 2017. "The multiplier effect in two-sided markets with bilateral investments," Working Paper Series in Economics 109, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    8. Per Hjertstrand, 2023. "On the Curvature of Homogeneous Functions," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 215-223, July.
    9. Tamás L. Balogh & Christian Ewerhart, 2015. "On the origin of r-concavity and related concepts," ECON - Working Papers 187, Department of Economics - University of Zurich.
    10. Maslov, Alexander & Noiset, Luc & Schwartz, Jesse A., 2022. "A closer look at two conjectures about irregular marginal revenue," Economics Letters, Elsevier, vol. 218(C).
    11. Haitian Xie, 2023. "Grenander-type Density Estimation under Myerson Regularity," Papers 2305.09052, arXiv.org.

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    More about this item

    Keywords

    Virtual valuation; Regularity; Generalized concavity; Prékopa–Borell theorem; Mechanism design; D82; D44; D86; C16;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

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