Optimal Mechanisms for Value Maximizers with Budget Constraints via Target Clipping

34 Pages Posted: 27 Apr 2022

See all articles by Santiago Balseiro

Santiago Balseiro

Columbia University - Columbia Business School, Decision Risk and Operations

Yuan Deng

Google Research

Jieming Mao

Google Research

Vahab Mirrokni

Google Inc.

Song Zuo

Google Inc.

Date Written: February 10, 2022

Abstract

We study the design of revenue-maximizing mechanisms for value-maximizing agents with budget constraints. Agents have return-on-spend constraints requiring a minimum amount of value per unit of payment made and budget constraints limiting their total payments. The agents' only private information are the minimum admissible ratios on the return-on-spend constraint, referred to as the target ratios.

Our work is motivated by internet advertising platforms, where automated bidders are increasingly being adopted by advertisers to purchase advertising opportunities on their behalf. Instead of specifying bids for each keyword, advertiser set high-level goals, such as maximizing clicks, and targets on cost-per-clicks or return-on-spend, and the platform automatically purchases opportunities by bidding in different auctions. We present a model that abstracts away the complexities of the auto-bidding procurement process that is general enough to accommodate many allocation mechanisms such as auctions, matchings, etc.

We reduce the mechanism design problem when agents have private target ratios to a challenging non-linear optimization problem with monotonicity constraints. We provide a novel decomposition approach to tackle this problem that yields insights into the structure of optimal mechanisms and show that surprising features stem from the interaction on budget and return-on-spend constraints. Our optimal mechanism, which we dub the target-clipping mechanism, has an appealing structure: it sets a threshold on the target ratio of each agent, targets above the threshold are allocated efficiently, and targets below are clipped to the threshold.

Keywords: internet advertising, autobidding, mechanism design, value maximization, budget constraints, return-on-spend constraints

Suggested Citation

Balseiro, Santiago and Deng, Yuan and Mao, Jieming and Mirrokni, Vahab and Zuo, Song, Optimal Mechanisms for Value Maximizers with Budget Constraints via Target Clipping (February 10, 2022). Available at SSRN: https://ssrn.com/abstract=4081457 or http://dx.doi.org/10.2139/ssrn.4081457

Santiago Balseiro (Contact Author)

Columbia University - Columbia Business School, Decision Risk and Operations ( email )

3022 Broadway
New York, NY 10027
United States

Yuan Deng

Google Research ( email )

United States

Jieming Mao

Google Research ( email )

United States

Vahab Mirrokni

Google Inc. ( email )

1600 Amphitheatre Parkway
Second Floor
Mountain View, CA 94043
United States

Song Zuo

Google Inc. ( email )

Beijing
China

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