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Single and Multi-Dimensional Optimal Auctions - A Network Approach

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  • Alexey Malakhov
  • Rakesh V. Vohra

Abstract

This paper highlights connections between the discrete and continuous approaches to optimal auction design with single and multi-dimensional types. We provide an interpretaion of an optimal auction design problem in terms of a linear program that is an instance of a parametric shortest path problem on a lattice. We also solve some cases explicitly in the discrete framework.

Suggested Citation

  • Alexey Malakhov & Rakesh V. Vohra, 2004. "Single and Multi-Dimensional Optimal Auctions - A Network Approach," Discussion Papers 1397, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:1397
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    File URL: http://www.kellogg.northwestern.edu/research/math/papers/1397.pdf
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    References listed on IDEAS

    as
    1. Jean-Charles Rochet & Philippe Chone, 1998. "Ironing, Sweeping, and Multidimensional Screening," Econometrica, Econometric Society, vol. 66(4), pages 783-826, July.
    2. Vijay Krishna & Motty Perry, 1997. "Efficient Mechanism Design," Game Theory and Information 9703010, University Library of Munich, Germany, revised 28 Apr 1998.
    3. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    4. Rochet, Jean-Charles, 1987. "A necessary and sufficient condition for rationalizability in a quasi-linear context," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 191-200, April.
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    Citations

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    Cited by:

    1. Penna, Paolo & Ventre, Carmine, 2014. "Optimal collusion-resistant mechanisms with verification," Games and Economic Behavior, Elsevier, vol. 86(C), pages 491-509.
    2. Garud Iyengar & Anuj Kumar, 2008. "Optimal procurement mechanisms for divisible goods with capacitated suppliers," Review of Economic Design, Springer;Society for Economic Design, vol. 12(2), pages 129-154, June.
    3. Olivier Bochet, 2007. "Implementation of the Walrasian correspondence: the boundary problem," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(2), pages 301-316, October.
    4. Myerson, Roger B., 2007. "Virtual utility and the core for games with incomplete information," Journal of Economic Theory, Elsevier, vol. 136(1), pages 260-285, September.
    5. Mallesh Pai & Rakesh Vohra, 2008. "Optimal Dynamic Auctions," Discussion Papers 1461, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    6. Jung, Jihyeok & Song, Chan-Oi & Lee, Deok-Joo & Yoon, Kiho, 2024. "Optimal energy procurement with long-term photovoltaic energy contracts considering generation uncertainty: A two-dimensional auction approach," Applied Energy, Elsevier, vol. 356(C).
    7. Chaithanya Bandi & Dimitris Bertsimas, 2014. "Optimal Design for Multi-Item Auctions: A Robust Optimization Approach," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1012-1038, November.
    8. Alexey Malakhov & Rakesh Vohra, 2009. "An optimal auction for capacity constrained bidders: a network perspective," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(1), pages 113-128, April.

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    More about this item

    Keywords

    Auctions; Networks; Linear Programming;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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