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Optimal combinatorial mechanism design

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  • Levent Ülkü

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

Suggested Citation

  • Levent Ülkü, 2013. "Optimal combinatorial mechanism design," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(2), pages 473-498, June.
    • Handle: RePEc:spr:joecth:v:53:y:2013:i:2:p:473-498
    DOI: 10.1007/s00199-012-0700-8
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    Cited by:

    1. Meng, Xin & Gunay, Hikmet, 2017. "Exposure problem in multi-unit auctions," International Journal of Industrial Organization, Elsevier, vol. 52(C), pages 165-187.
    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," CIRJE F-Series CIRJE-F-955, CIRJE, Faculty of Economics, University of Tokyo.
    4. Hitoshi Matsushima, 2018. "Optimal Deterministic Mechanism Design: Type-Independent Preference Orderings," The Japanese Economic Review, Springer, vol. 69(4), pages 363-373, December.
    5. 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.
    6. Hitoshi Matsushima, 2015. "Optimal Mechanism Design: Type-Independent Preference Orderings (Published in the Japanese Economic Review 69 (4), 2018.)," CARF F-Series CARF-F-357, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    7. Yi Zhu & Kenneth C. Wilbur, 2011. "Hybrid Advertising Auctions," Marketing Science, INFORMS, vol. 30(2), pages 249-273, 03-04.
    8. Gomes, Renato & Sweeney, Kane, 2014. "Bayes–Nash equilibria of the generalized second-price auction," Games and Economic Behavior, Elsevier, vol. 86(C), pages 421-437.
    9. 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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    More about this item

    Keywords

    Combinatorial mechanism design; Interdependent values; Supermodularity; Regularity; C70; D44; D60; D82;
    All these keywords.

    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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