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

## Author

Listed:
• 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

## Suggested Citation

• 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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File URL: http://hdl.handle.net/10.1007/s00199-012-0705-3

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## References listed on IDEAS

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## Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
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Cited by:

1. Ryan Cumings, 2017. "Shape-Constrained Density Estimation Via Optimal Transport," Papers 1710.09069, arXiv.org.

### Keywords

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

### 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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