Platform Competition in the Autobidding World

TL;DR

This paper analyzes cross-platform auction design in a setting where value-maximizing advertisers with ROI constraints bid across multiple autobidder-enabled platforms that use uniform bidding. It shows that platform competition profoundly alters the optimal auction format: while first-price auctions maximize welfare and revenue in a single-platform world, second-price auctions can dominate in multi-platform environments depending on advertiser elasticity, competition intensity, and SPA-FPA inefficiency. The advertiser bidding subgame is characterized by marginal-cost equalization across platforms, with equilibria detailed for symmetric and asymmetric platform configurations. The findings have practical implications for platform designers, emphasizing the need to account for advertiser responses and inter-platform externalities when switching auction formats.

Abstract

We study the problem of auction design for advertising platforms that face strategic advertisers who are bidding across platforms. Each advertiser's goal is to maximize their total value or conversions while satisfying some constraint(s) across all the platforms they participates in. In this paper, we focus on advertisers with return-over-investment (henceforth, ROI) constraints, i.e. each advertiser is trying to maximize value while making sure that their ROI across all platforms is no less than some target value. An advertiser interacts with the platforms through autobidders -- for each platform, the advertiser strategically chooses a target ROI to report to the platform's autobidder, which in turn uses a uniform bid multiplier to bid on the advertiser's behalf on the queries owned by the given platform. Our main result is that for a platform trying to maximize revenue, competition with other platforms is a key factor to consider when designing their auction. While first-price auctions are optimal (for both revenue and welfare) in the absence of competition, this no longer holds true in multi-platform settings. We show that there exists a large class of advertiser valuations over queries such that, from the platform's perspective, running a second price auction dominates running a first price auction. Furthermore, our analysis reveals the key factors influencing platform choice of auction format: (i) intensity of competition among advertisers, (ii) sensitivity of bid landscapes to an auction change (driven by advertiser sensitivity to price changes), and (iii) relative inefficiency of second-price auctions compared to first-price auctions.

Figures (12)

• Figure 1: This figure captures the different agents (advertiser, platforms) involved in the game we are interested in studying. Advertiser $i$ submits target $T_{ij}$ to Autobidder $ij$, who bids on the their behalf on Platform $j$.
• Figure 2: An illustration of the advertiser equilibrium in each profile.
• Figure 3: Plot of valuations $v_1(q) = \alpha q$ (for $\alpha = 2.5$) and $v_2(q) = 1$.
• Figure 4: This plot shows the efficiency of the FP and SP platforms on the (SPA, FPA) subgame.
• Figure 5: This plot shows the competition metric $\mathcal{C}^\mathcal{A}$ as a function $\alpha$ for the case of a linear and constant-valued advertiser.

Theorems & Definitions (79)

• Remark 2.1
• Definition 2.3: Liquid Welfare
• Remark 2.4
• Definition 2.5: Competition
• Theorem 3.2
• Lemma 3.3
• Theorem 3.4
• Theorem 3.5
• Corollary 3.6
• Theorem 3.7: (FPA, FPA) subgame yuan_towards