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Optimal combinatorial mechanism design

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  • Levent Ülkü

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Abstract

We consider an optimal mechanism design problem with several heterogenous objects and interdependent values. We characterize ex post incentives using an appropriate monotonicity condition and reformulate the problem in such a way that the choice of an allocation rule can be separated from the choice of the payment rule. Central to the analysis is the formulation of a regularity condition, which gives a recipe for the optimal mechanism. If the problem is regular, then an optimal mechanism can be obtained by solving a combinatorial allocation problem in which objects are allocated in a way to maximize the sum of virtual valuations. We identify conditions that imply regularity using the techniques of supermodular optimization. Copyright Springer-Verlag 2013

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File URL: http://hdl.handle.net/10.1007/s00199-012-0700-8
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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 53 (2013)
Issue (Month): 2 (June)
Pages: 473-498

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Handle: RePEc:spr:joecth:v:53:y:2013:i:2:p:473-498

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Related research

Keywords: Combinatorial mechanism design; Interdependent values; Supermodularity; Regularity; C70; D44; D60; D82;

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  1. Fernando Branco, 1996. "Multiple unit auctions of an indivisible good," Economic Theory, Springer, vol. 8(1), pages 77-101.
  2. Eric Maskin & John Riley, 1984. "Monopoly with Incomplete Information," RAND Journal of Economics, The RAND Corporation, vol. 15(2), pages 171-196, Summer.
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  4. Krishna, Vijay, 2003. "Asymmetric English auctions," Journal of Economic Theory, Elsevier, vol. 112(2), pages 261-288, October.
  5. Krishna, Vijay & Maenner, Eliot, 2001. "Convex Potentials with an Application to Mechanism Design," Econometrica, Econometric Society, vol. 69(4), pages 1113-19, July.
  6. Monteiro, Paulo Klinger, 1999. "Optimal Auctions in a General Model of Identical Goods," Economics Working Papers (Ensaios Economicos da EPGE) 358, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  7. Levin, Jonathan, 1997. "An Optimal Auction for Complements," Games and Economic Behavior, Elsevier, vol. 18(2), pages 176-192, February.
  8. Lawrence M. Ausubel & Peter Cramton, 1998. "The Optimality of Being Efficient," Papers of Peter Cramton 98wpoe, University of Maryland, Department of Economics - Peter Cramton, revised 18 Jun 1999.
  9. Cremer, Jacques & McLean, Richard P, 1985. "Optimal Selling Strategies under Uncertainty for a Discriminating Monopolist When Demands Are Interdependent," Econometrica, Econometric Society, vol. 53(2), pages 345-61, March.
  10. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January.
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Cited by:
  1. Hitoshi Matsushima, 2012. "Optimal Multiunit Exchange Design with Single-Dimensionality," CARF F-Series CARF-F-292, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Sep 2012.
  2. Benjamin Edelman & Michael Schwarz, 2010. "Optimal Auction Design and Equilibrium Selection in Sponsored Search Auctions," American Economic Review, American Economic Association, vol. 100(2), pages 597-602, May.

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