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Overbidding and underbidding in package allocation problems

Author

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  • Marina Núñez

    (Universitat de Barcelona)

  • Francisco Robles

    (Universitat de Barcelona)

Abstract

We study the problem of allocating packages of different objects to a group of bidders. A rule is overbidding-proof if no bidder has incentives to bid above his actual valuations. We prove that if an efficient rule is overbidding-proof, then each winning bidder pays a price between his winning bid and what he would pay in a Vickrey auction for the same package. In counterpart, the set of rules that satisfy underbidding-proofness always charge a price below the corresponding Vickrey price. A new characterization of the Vickrey allocation rule is provided with a weak form of strategy-proofness. The Vickrey rule is the only rule that satisfies efficiency, individual rationality, overbidding-proofness and underbidding-proofness. Our results are also valid on the domains of monotonic valuations and of single-minded bidders. Finally a family of overbidding rules is introduced that price the assigned packages at a fixed average of the Vickrey price and the pay-as-bid price.

Suggested Citation

  • Marina Núñez & Francisco Robles, 2024. "Overbidding and underbidding in package allocation problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 62(4), pages 739-759, June.
    • Handle: RePEc:spr:sochwe:v:62:y:2024:i:4:d:10.1007_s00355-024-01506-5
    DOI: 10.1007/s00355-024-01506-5
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    References listed on IDEAS

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    1. Kagel, John H. & Levin, Dan, 2009. "Implementing efficient multi-object auction institutions: An experimental study of the performance of boundedly rational agents," Games and Economic Behavior, Elsevier, vol. 66(1), pages 221-237, May.
    2. B. Douglas Bernheim & Michael D. Whinston, 1986. "Menu Auctions, Resource Allocation, and Economic Influence," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 101(1), pages 1-31.
    3. Ausubel Lawrence M & Milgrom Paul R, 2002. "Ascending Auctions with Package Bidding," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-44, August.
    4. Kagel, John H & Levin, Dan, 1993. "Independent Private Value Auctions: Bidder Behaviour in First-, Second- and Third-Price Auctions with Varying Numbers of Bidders," Economic Journal, Royal Economic Society, vol. 103(419), pages 868-879, July.
    5. Robert Day & Paul Milgrom, 2008. "Core-selecting package auctions," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 393-407, March.
    6. Benjamin Edelman & Michael Ostrovsky & Michael Schwarz, 2007. "Internet Advertising and the Generalized Second-Price Auction: Selling Billions of Dollars Worth of Keywords," American Economic Review, American Economic Association, vol. 97(1), pages 242-259, March.
    7. Alvin E. Roth, 2002. "The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics," Econometrica, Econometric Society, vol. 70(4), pages 1341-1378, July.
    8. Bikhchandani, Sushil & Ostroy, Joseph M., 2002. "The Package Assignment Model," Journal of Economic Theory, Elsevier, vol. 107(2), pages 377-406, December.
    9. Kagel, John H & Harstad, Ronald M & Levin, Dan, 1987. "Information Impact and Allocation Rules in Auctions with Affiliated Private Values: A Laboratory Study," Econometrica, Econometric Society, vol. 55(6), pages 1275-1304, November.
    10. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2016. "Group Strategy-Proofness in Private Good Economies," American Economic Review, American Economic Association, vol. 106(4), pages 1073-1099, April.
    11. Kagel, John H. & Lien, Yuanchuan & Milgrom, Paul, 2014. "Ascending prices and package bidding: Further experimental analysis," Games and Economic Behavior, Elsevier, vol. 85(C), pages 210-231.
    12. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521536721, December.
    13. Bae, Jinsoo & Kagel, John H., 2019. "An experimental study of the generalized second price auction," International Journal of Industrial Organization, Elsevier, vol. 63(C), pages 44-68.
    14. Estelle Cantillon & Martin Pesendorfer, 2006. "Auctioning bus routes: the London experience," ULB Institutional Repository 2013/9003, ULB -- Universite Libre de Bruxelles.
    15. Paul Milgrom, 2007. "Package Auctions and Exchanges," Econometrica, Econometric Society, vol. 75(4), pages 935-965, July.
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    Cited by:

    1. Francisco Robles & Marina Núñez & Laura Robles, 2024. "Monotonic transformation of preferences and Walrasian equilibrium in allocation problems," UB School of Economics Working Papers 2024/478, University of Barcelona School of Economics.

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