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Auctions without commitment in the auto-bidding world

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  • Aranyak Mehta
  • Andres Perlroth

Abstract

Advertisers in online ad auctions are increasingly using auto-bidding mechanisms to bid into auctions instead of directly bidding their value manually. One prominent auto-bidding format is the target cost-per-acquisition (tCPA) which maximizes the volume of conversions subject to a return-of-investment constraint. From an auction theoretic perspective however, this trend seems to go against foundational results that postulate that for profit-maximizing bidders, it is optimal to use a classic bidding system like marginal CPA (mCPA) bidding rather than using strategies like tCPA. In this paper we rationalize the adoption of such seemingly sub-optimal bidding within the canonical quasi-linear framework. The crux of the argument lies in the notion of commitment. We consider a multi-stage game where first the auctioneer declares the auction rules; then bidders select either the tCPA or mCPA bidding format and then, if the auctioneer lacks commitment, it can revisit the rules of the auction (e.g., may readjust reserve prices depending on the observed bids). Our main result is that so long as a bidder believes that the auctioneer lacks commitment to follow the rule of the declared auction then the bidder will make a higher profit by choosing the tCPA format over the mCPA format. We then explore the commitment consequences for the auctioneer. In a simplified version of the model where there is only one bidder, we show that the tCPA subgame admits a credible equilibrium while the mCPA format does not. That is, when the bidder chooses the tCPA format the auctioneer can credibly implement the auction rules announced at the beginning of the game. We also show that, under some mild conditions, the auctioneer's revenue is larger when the bidder uses the tCPA format rather than mCPA. We further quantify the value for the auctioneer to be able to commit to the declared auction rules.

Suggested Citation

  • Aranyak Mehta & Andres Perlroth, 2023. "Auctions without commitment in the auto-bidding world," Papers 2301.07312, arXiv.org, revised Mar 2023.
    • Handle: RePEc:arx:papers:2301.07312
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    References listed on IDEAS

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    1. Bester, Helmut & Strausz, Roland, 2000. "Imperfect commitment and the revelation principle: the multi-agent case," Economics Letters, Elsevier, vol. 69(2), pages 165-171, November.
    2. Che, Yeon-Koo & Gale, Ian, 2000. "The Optimal Mechanism for Selling to a Budget-Constrained Buyer," Journal of Economic Theory, Elsevier, vol. 92(2), pages 198-233, June.
    3. Bester, Helmut & Strausz, Roland, 2001. "Contracting with Imperfect Commitment and the Revelation Principle: The Single Agent Case," Econometrica, Econometric Society, vol. 69(4), pages 1077-1098, July.
    4. Santiago R. Balseiro & Yonatan Gur, 2019. "Learning in Repeated Auctions with Budgets: Regret Minimization and Equilibrium," Management Science, INFORMS, vol. 65(9), pages 3952-3968, September.
    5. Gul, Faruk & Sonnenschein, Hugo & Wilson, Robert, 1986. "Foundations of dynamic monopoly and the coase conjecture," Journal of Economic Theory, Elsevier, vol. 39(1), pages 155-190, June.
    6. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    7. Laffont, Jean-Jacques & Robert, Jacques, 1996. "Optimal auction with financially constrained buyers," Economics Letters, Elsevier, vol. 52(2), pages 181-186, August.
    8. Matheus V. X. Ferreira & S. Matthew Weinberg, 2020. "Credible, Truthful, and Two-Round (Optimal) Auctions via Cryptographic Commitments," Papers 2004.01598, arXiv.org, revised May 2020.
    9. Mohammad Akbarpour & Shengwu Li, 2020. "Credible Auctions: A Trilemma," Econometrica, Econometric Society, vol. 88(2), pages 425-467, March.
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    Cited by:

    1. Yiding Feng & Brendan Lucier & Aleksandrs Slivkins, 2023. "Strategic Budget Selection in a Competitive Autobidding World," Papers 2307.07374, arXiv.org, revised Nov 2023.
    2. Yeganeh Alimohammadi & Aranyak Mehta & Andres Perlroth, 2023. "Incentive Compatibility in the Auto-bidding World," Papers 2301.13414, arXiv.org, revised May 2024.

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