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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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