Simultaneous 2nd price item auctions with no-underbidding

Michal Feldman, Galia Shabtai*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The literature on the Price of Anarchy (PoA) of simple auctions employs a no-overbidding assumption but has completely overlooked the no-underbidding phenomenon, which is evident in empirical studies on variants of the second price auction. In this work, we provide a theoretical foundation for the no-underbidding phenomenon. We study the PoA of simultaneous 2nd price auctions (S2PA) under a new natural condition of no underbidding, meaning that agents never bid on items less than their marginal values. We establish improved (mostly tight) bounds on the PoA of S2PA under no-underbidding for different valuation classes, in both full-information and incomplete information settings. Specifically, we show that the PoA is at least 1/2 for general monotone valuations, which extends to Bayesian PoA with arbitrary correlated distributions. We also establish a tight PoA bound of 2/3 for S2PA with XOS valuations, under no-overbidding and no-underbidding, which extends to Bayesian PoA with independent distributions.

Original languageEnglish
Pages (from-to)316-340
Number of pages25
JournalGames and Economic Behavior
Volume140
DOIs
StatePublished - Jul 2023

Funding

FundersFunder number
European Research Council
Israel Science Foundation1219/09
Horizon 2020866132

    Keywords

    • Algorithmic game theory
    • Price of anarchy
    • Simultaneous item bidding auctions

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