Budget-Constrained Auctions with Unassured Priors: Strategic Equivalence and Structural Properties

52 Pages Posted: 29 Apr 2022 Last revised: 6 Dec 2022

See all articles by Zhaohua Chen

Zhaohua Chen

Peking University

Xiaotie Deng

Peking University

Jicheng Li

University of Virginia

Chang Wang

Peking University

Mingwei Yang

Peking University - Department of Computer Science and Technology

Zheng Cai

affiliation not provided to SSRN

Yukun Ren

affiliation not provided to SSRN

Zhihua Zhu

affiliation not provided to SSRN

Date Written: December 6, 2022

Abstract

In today's online advertising markets, it is common for an advertiser to set a long-period budget. Correspondingly, advertising platforms adopt budget control methods to ensure that an advertiser's payment is within her budget. Most budget control methods rely on the value distributions of advertisers. However, the platform hardly learns their true priors due to the complex environment advertisers stand in and privacy issues. Therefore, it is essential to understand how budget control auction mechanisms perform under unassured priors.

This work answers this problem from multiple aspects. Specifically, we discuss five budget-constrained parameterized mechanisms: bid-discount/pacing first-price auctions, the Bayesian revenue-optimal auction and bid-discount/pacing second-price auctions. We consider the game among the seller and all buyers induced by these five mechanisms in the stochastic model. We restrict the discussion to efficient mechanisms in which the seller earns buyers' budgets sufficiently, and thus, leads to his high revenue. Our main result shows the strategic equivalence between the Bayesian revenue-optimal mechanism and the efficient bid-discount first-price mechanism. A broad equivalence among all these (efficient) mechanisms is also given in the symmetric case. We further dig into the structural properties of stochastic budget-constrained mechanisms. We characterize sufficient and necessary conditions on the efficient parameter tuple for bid-discount/pacing first-price auctions. Meanwhile, when buyers do not take strategic behaviors, we exploit the dominance relationships of these mechanisms by revealing their intrinsic structures.

Suggested Citation

Chen, Zhaohua and Deng, Xiaotie and Li, Jicheng and Wang, Chang and Yang, Mingwei and Cai, Zheng and Ren, Yukun and Zhu, Zhihua, Budget-Constrained Auctions with Unassured Priors: Strategic Equivalence and Structural Properties (December 6, 2022). Available at SSRN: https://ssrn.com/abstract=4071291 or http://dx.doi.org/10.2139/ssrn.4071291

Zhaohua Chen (Contact Author)

Peking University ( email )

Xiaotie Deng

Peking University ( email )

Jicheng Li

University of Virginia ( email )

1400 University Ave
Charlottesville, VA 22903
United States

Chang Wang

Peking University ( email )

No. 38 Xueyuan Road
Haidian District
Beijing, Beijing 100871
China

Mingwei Yang

Peking University - Department of Computer Science and Technology ( email )

Beijing
China

Zheng Cai

affiliation not provided to SSRN

Yukun Ren

affiliation not provided to SSRN

Zhihua Zhu

affiliation not provided to SSRN

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
15
Abstract Views
173
PlumX Metrics