A geometric approach to mechanism design
AbstractWe 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.
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Bibliographic InfoPaper provided by Department of Economics - University of Zurich in its series ECON - Working Papers with number 056.
Date of creation: Dec 2011
Date of revision: Jun 2013
Mechanism design; convex set; support function; duality; majorization; ironing; Hotelling's lemma; reduced-from implementation; BIC-DIC equivalence; concave objectives; interdependent values; second-best mechanisms;
Find related papers by JEL classification:
- D44 - Microeconomics - - Market Structure and Pricing - - - Auctions
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-01-03 (All new papers)
- NEP-CTA-2012-01-03 (Contract Theory & Applications)
- NEP-MIC-2012-01-03 (Microeconomics)
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.:
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