Optimal Information Design for Click-Through Auctions with Bayesian Bidders

Core Concepts

The seller can partially reveal information about bidders' click-through rates to maximize revenue in click-through auctions, while maintaining calibration constraints.

Abstract

The paper studies the problem of optimal information design in click-through auctions, where the seller has private information about bidders' click-through rates (CTRs) and can partially reveal this information to maximize revenue. This is a Bayesian variant of the "calibrated click-through auctions" studied by Bergemann et al. [11]. The key insights are: Information design in click-through auctions is different from previous studies, as the revealed information affects the auction's allocation and payment rule, but not the bidders' bidding behaviors. For the general case with a constant number of bidders, the authors provide an FPTAS to compute an approximately optimal signaling scheme, leveraging the Lipschitz continuity of the revenue function. For the symmetric two-bidder case, the authors characterize the optimal signal ratio and construct a simple, prior-free signaling scheme that achieves a 0.995 approximation ratio, as long as the bidders' value density functions do not fluctuate much. The technical contributions include novel discretization techniques to handle the calibration constraints, and a connection between the optimal signaling scheme under unknown value distributions and the uniform distribution.

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Key Insights Distilled From

Bayesian Calibrated Click-Through Auction

by Junjie Chen,... at arxiv.org 04-23-2024

https://arxiv.org/pdf/2306.06554.pdf

Deeper Inquiries

How can the proposed information design techniques be extended to more complex auction formats, such as multi-slot auctions or auctions with budget-constrained bidders

The proposed information design techniques can be extended to more complex auction formats by adapting the signaling schemes to accommodate the specific characteristics of these auctions. For multi-slot auctions, where multiple items are being auctioned simultaneously, the signaling scheme can be modified to consider the allocation of multiple slots to different bidders. This would involve designing signals that reveal information about the optimal allocation of slots based on the bidders' values and the auctioneer's knowledge. In auctions with budget-constrained bidders, the signaling scheme can be tailored to provide information that helps bidders make optimal bidding decisions within their budget constraints. This could involve signaling the expected return on investment for different bid amounts, taking into account the bidders' budget limitations. Overall, the extension to more complex auction formats would require a careful analysis of the specific auction dynamics and constraints to design signaling schemes that maximize revenue while ensuring truthful bidding behavior from the bidders.

What are the implications of the optimal signal ratio being at most 1

The implication of the optimal signal ratio being at most 1 is that the signaling scheme tends to focus on providing information that aligns with the bidders' true values rather than overly specific or targeted information. This limitation on the signal ratio prevents the signaling scheme from becoming too persuasive or manipulative, ensuring that bidders continue to bid truthfully based on their actual values per click. This observation relates to the concept that too "fine-grained" targeting information may lead to a thin market. When information provided to bidders becomes too specific or tailored, it can reduce competition in the auction by discouraging certain bidders from participating. By limiting the signal ratio to be at most 1, the signaling scheme strikes a balance between providing relevant information to bidders and maintaining a competitive auction environment.

How does this relate to the observation that too "fine-grained" targeting information may lead to a thin market

The insights from this work on click-through auctions can be applied to other settings where the revealed information affects the mechanism but not the agents' behaviors. One such application could be in personalized pricing strategies, where the seller uses information about the buyer's preferences or willingness to pay to optimize pricing decisions. In this context, the seller can design signaling schemes that reveal personalized pricing options based on the buyer's characteristics, without influencing the buyer's decision-making process. By leveraging the principles of information design from click-through auctions, the seller can maximize revenue by offering tailored pricing options while ensuring that buyers continue to make decisions based on their true valuation of the product or service.