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Bidding in Simultaneous Auctions with a Constraint on Exposure

Author

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  • Michael H. Rothkopf

    (Xerox Corporation, Palo Alto, California)

Abstract

We consider the problem of determining a profit maximizing set of sealed bids in simultaneous auctions that are independent except for a restriction on the total of all bids. Although the objective function is not concave, we show that a Lagrangian approach will often yield an optimal answer and, when it does not, will yield a good solution and a bound on possible further improvements. Characteristics of optimal sets of bids are proven. The methodology employed will be generally attractive for any problem that involves allocating a single resource among a large number of competing activities with convex-concave profit functions.

Suggested Citation

  • Michael H. Rothkopf, 1977. "Bidding in Simultaneous Auctions with a Constraint on Exposure," Operations Research, INFORMS, vol. 25(4), pages 620-629, August.
    • Handle: RePEc:inm:oropre:v:25:y:1977:i:4:p:620-629
    DOI: 10.1287/opre.25.4.620
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    Citations

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    Cited by:

    1. Dirk Alboth & Anat Lerner & Jonathan Shalev, 2001. "Profit Maximizing in Auctions of Public Goods," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 3(4), pages 501-525, October.
    2. Anne-Christine Barthel & Tarun Sabarwal, 2018. "Directional monotone comparative statics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 557-591, October.
    3. Muñoz, Juan Carlos & Molina, Diego, 2009. "A multi-unit tender award process: The case of Transantiago," European Journal of Operational Research, Elsevier, vol. 197(1), pages 307-311, August.
    4. Gerard van der Laan & Zaifu Yang, 2016. "An ascending multi-item auction with financially constrained bidders," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 109-149, December.
    5. Tommy Andersson & Lars Ehlers, 2022. "An algorithm for identifying least manipulable envy‐free and budget‐balanced allocations in economies with indivisibilities," International Journal of Economic Theory, The International Society for Economic Theory, vol. 18(1), pages 50-60, March.
    6. Srivastava, Vaibhav & Bullo, Francesco, 2014. "Knapsack problems with sigmoid utilities: Approximation algorithms via hybrid optimization," European Journal of Operational Research, Elsevier, vol. 236(2), pages 488-498.
    7. Michael H. Rothkopf & Aleksandar Pekev{c} & Ronald M. Harstad, 1998. "Computationally Manageable Combinational Auctions," Management Science, INFORMS, vol. 44(8), pages 1131-1147, August.
    8. Cramton, Peter C, 1995. "Money Out of Thin Air: The Nationwide Narrowband PCS Auction," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 4(2), pages 267-343, Summer.
    9. Sandholm, Tuomas & Suri, Subhash, 2006. "Side constraints and non-price attributes in markets," Games and Economic Behavior, Elsevier, vol. 55(2), pages 321-330, May.
    10. ALBOTH, Dirk & LERNER, Anat & SHALEV, Jonathan, 1997. "Auctioning public goods to groups of aghents," LIDAM Discussion Papers CORE 1997077, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. Lorentziadis, Panos L., 2016. "Optimal bidding in auctions from a game theory perspective," European Journal of Operational Research, Elsevier, vol. 248(2), pages 347-371.
    12. Elena Katok & Alvin E. Roth, 2004. "Auctions of Homogeneous Goods with Increasing Returns: Experimental Comparison of Alternative "Dutch" Auctions," Management Science, INFORMS, vol. 50(8), pages 1044-1063, August.
    13. repec:kan:wpaper:201502 is not listed on IDEAS
    14. Jin, Mingzhou & Wu, S. David & Erkoc, Murat, 2006. "Multiple unit auctions with economies and diseconomies of scale," European Journal of Operational Research, Elsevier, vol. 174(2), pages 816-834, October.
    15. Sunnevag, Kjell J., 2000. "Designing auctions for offshore petroleum lease allocation," Resources Policy, Elsevier, vol. 26(1), pages 3-16, March.
    16. repec:kan:wpaper:201412 is not listed on IDEAS

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