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Iterative Auction Design for Tree Valuations

Author

Listed:
  • Ozan Candogan

    (The University of Chicago Booth School of Business, Chicago, Illinois 60637)

  • Asuman Ozdaglar

    (Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Pablo A. Parrilo

    (Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

Abstract

We study a special class of multi-item valuations (tree valuations) that exhibit both value complementarity and substitutability. We provide a linear programming formulation of the efficient allocation problem that is of polynomial size in the number of agents and items. This reveals a new class of valuations for which a Walrasian equilibrium exists in the presence of value complementarities. An iterative algorithm for this linear program, in conjunction with an appropriate payment rule, yields an iterative auction that implements the efficient outcome (at an ex post perfect equilibrium). This auction relies on a simple pricing rule, compact demand reports, and uses a novel (interleaved) price update structure to assign final payments to bidders that guarantee truthful bidding.

Suggested Citation

  • Ozan Candogan & Asuman Ozdaglar & Pablo A. Parrilo, 2015. "Iterative Auction Design for Tree Valuations," Operations Research, INFORMS, vol. 63(4), pages 751-771, August.
    • Handle: RePEc:inm:oropre:v:63:y:2015:i:4:p:751-771
    DOI: 10.1287/opre.2015.1388
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    References listed on IDEAS

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    2. Tim Roughgarden, 2018. "Complexity Theory, Game Theory, and Economics: The Barbados Lectures," Papers 1801.00734, arXiv.org, revised Feb 2020.
    3. Elizabeth Baldwin & Omer Edhan & Ravi Jagadeesan & Paul Klemperer & Alexander Teytelboym, 2020. "The Equilibrium Existence Duality: Equilibrium with Indivisibilities & Income Effects," Papers 2006.16939, arXiv.org.
    4. Marzena Rostek & Nathan Yoder, 2020. "Matching With Complementary Contracts," Econometrica, Econometric Society, vol. 88(5), pages 1793-1827, September.
    5. Hideto Koizumi, 2023. "The enemy of my enemy is my friend: new conditions for network games," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(2), pages 223-233, October.
    6. Ozan Candogan & Saša Pekeč, 2018. "Efficient Allocation and Pricing of Multifeatured Items," Management Science, INFORMS, vol. 64(12), pages 5521-5543, December.
    7. Xiaoshuai Fan & Ying‐Ju Chen & Christopher S. Tang, 2021. "To Bribe or Not in a Procurement Auction under Disparate Corruption Pressure," Production and Operations Management, Production and Operations Management Society, vol. 30(5), pages 1220-1245, May.
    8. Marie-Charlotte Brandenburg & Christian Haase & Ngoc Mai Tran, 2021. "Competitive equilibrium always exists for combinatorial auctions with graphical pricing schemes," Papers 2107.08813, arXiv.org, revised Nov 2021.

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