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Optimal Combinatorial Mechanism Design

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  • Levent Ulku

    () (Centro de Investigacion Economica (CIE), Instituto Tecnologico Autonomo de Mexico (ITAM))

Abstract

We consider an optimal mechanism design problem with several heterogeneous 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 our 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 for two nonnested environments using the techniques of supermodular optimization.

Suggested Citation

  • Levent Ulku, 2009. "Optimal Combinatorial Mechanism Design," Working Papers 0903, Centro de Investigacion Economica, ITAM.
  • Handle: RePEc:cie:wpaper:0903
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    File URL: http://ftp.itam.mx/pub/academico/inves/ulku/09-03.pdf
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    References listed on IDEAS

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    1. Fernando Branco, 1996. "Multiple unit auctions of an indivisible good," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 77-101.
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    5. Eric Maskin & John Riley, 1984. "Monopoly with Incomplete Information," RAND Journal of Economics, The RAND Corporation, vol. 15(2), pages 171-196, Summer.
    6. Krishna, Vijay, 2003. "Asymmetric English auctions," Journal of Economic Theory, Elsevier, vol. 112(2), pages 261-288, October.
    7. 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.
    8. Monteiro, Paulo Klinger, 2002. "Optimal auctions in a general model of identical goods," Journal of Mathematical Economics, Elsevier, vol. 37(1), pages 71-79, February.
    9. Levin, Jonathan, 1997. "An Optimal Auction for Complements," Games and Economic Behavior, Elsevier, vol. 18(2), pages 176-192, February.
    10. 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 345-361, March.
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    Cited by:

    1. Hikmet Gunay & Xin Meng, 2012. "Exposure Problem in Multi-unit Auctions," ISER Discussion Paper 0848, Institute of Social and Economic Research, Osaka University.
    2. Ruben Juarez & Rajnish Kumar, 2013. "Implementing efficient graphs in connection networks," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(2), pages 359-403, October.
    3. Hitoshi Matsushima, 2015. "Optimal Mechanism Design: Type-Independent Preference Orderings," CARF F-Series CARF-F-357, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    4. 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.
    5. repec:eee:indorg:v:52:y:2017:i:c:p:165-187 is not listed on IDEAS
    6. 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.

    More about this item

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D60 - Microeconomics - - Welfare Economics - - - General
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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