A geometric approach to mechanism design
We develop a novel geometric approach to mechanism design using an important result in convex analysis: the duality between a closed convex set and its support function. By deriving the support function for the set of feasible interim values we extend the wellknown Maskin-Riley-Matthews-Border conditions for reduced-form auctions to social choice environments. We next refine the support function to include incentive constraints using a geometric characterization of incentive compatibility. Borrowing results from majorization theory that date back to the work of Hardy, Littlewood, and Polya (1929) we elucidate the "ironing" procedure introduced by Myerson (1981) and Mussa and Rosen (1978). The inclusion of Bayesian and dominant strategy incentive constraints result in the same support function, which establishes equivalence between these implementation concepts. Using Hotelling's lemma we next derive the optimal mechanism for any social choice problem and any linear objective, including revenue and surplus maximization. We extend the approach to include general concave objectives by providing a fixed-point condition characterizing the optimal mechanism. We generalize reduced-form implementation to environments with multi-dimensional, correlated types, non-linear utilities, and interdependent values. When value interdependencies are linear we are able to include incentive constraints into the support function and provide a condition when the second-best allocation is ex post incentive compatible.
|Date of creation:||Dec 2011|
|Date of revision:||Jun 2013|
|Contact details of provider:|| Postal: |
Phone: +41-1-634 21 37
Fax: +41-1-634 49 82
Web page: http://www.econ.uzh.ch/
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Simo Puntanen, 2011. "Inequalities: Theory of Majorization and Its Applications, Second Edition by Albert W. Marshall, Ingram Olkin, Barry C. Arnold," International Statistical Review, International Statistical Institute, vol. 79(2), pages 293-293, 08.
- Jacob K. Goeree & Alexey Kushnir, 2011. "On the equivalence of Bayesian and dominant strategy implementation in a general class of social choice problems," ECON - Working Papers 021, Department of Economics - University of Zurich.
- Hernando-Veciana, Ángel & Michelucci, Fabio, 2011. "Second best efficiency and the English auction," Games and Economic Behavior, Elsevier, vol. 73(2), pages 496-506.
- Martin F. Hellwig, 2003.
"Public-Good Provision with Many Participants,"
Review of Economic Studies,
Oxford University Press, vol. 70(3), pages 589-614.
- Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2011. "Bayesian and Dominant Strategy Implementation Revisited," Working Papers tecipa-422, University of Toronto, Department of Economics.
- Alejandro M. Manelli & Daniel R. Vincent, 2010. "Bayesian and Dominant‐Strategy Implementation in the Independent Private‐Values Model," Econometrica, Econometric Society, vol. 78(6), pages 1905-1938, November.
When requesting a correction, please mention this item's handle: RePEc:zur:econwp:056. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Marita Kieser)
If references are entirely missing, you can add them using this form.