Shill-Proof Auctions (2404.00475v2)

Abstract: In an auction, a seller may masquerade as one or more bidders in order to manipulate the clearing price. We characterize single-item auction formats that are shill-proof in the sense that a profit-maximizing seller has no incentive to submit shill bids. We distinguish between strong shill-proofness, in which a seller with full knowledge of bidders' valuations can never profit from shilling, and weak shill-proofness, which requires only that the expected equilibrium profit from shilling is nonpositive. The Dutch auction (with a suitable reserve) is the unique (revenue-)optimal and strongly shill-proof auction. Moreover, the Dutch auction (with no reserve) is the unique prior-independent auction that is both efficient and weakly shill-proof. While there are multiple ex-post incentive compatible, weakly shill-proof, and optimal auctions; any optimal auction can satisfy only two properties in the set {static, ex-post incentive compatible, weakly shill-proof}.

• The paper analyzes various auction formats to define and achieve strong or weak shill-proofness, aiming to prevent sellers from profiting through shill bidding.
• The paper finds the Dutch auction is uniquely optimal and strongly shill-proof, maximizing seller revenue while preventing profitable shill bids, though optimal auctions may trade off strategy-proofness.
• Ensuring auction shill-proofness often requires trading off strategy-proofness and efficiency, especially in static formats, revealing inherent complexities in robust auction design.

An Overview of "Shill-Proof Auctions"

This paper explores the design of auction mechanisms that deter sellers from participating in shill bidding—a deceptive practice where the seller places fake bids to manipulate the auction outcome. The authors rigorously analyze auction formats to determine which ensure shill-proofness under varying informational assumptions and preferences.

Key Contributions

1. Auction Formats and Shill-Proofness: The authors introduce two levels of shill-proofness: strong and weak. Strong shill-proofness occurs when, even with full bidder valuation knowledge, a seller cannot profit from shill bidding. Weak shill-proofness requires only that under equilibrium, the expected benefit from shill bidding is nonpositive.
2. Optimal and Shill-Proof Auctions: The Dutch auction, with a suitable reserve price, emerges uniquely optimal and strongly shill-proof. This means it maximizes seller revenue while ensuring no profitable shill bids, given full bidder valuation access. The paper finds that such optimal auctions must be iterative and cannot be strategy-proof.
3. Efficiency in Auctions: For efficient and weakly shill-proof auctions, the Dutch auction also holds significance. It is the sole prior-independent design that maintains efficiency while being weakly shill-proof. This robustness to valuation distribution details is partially why variants like the hybrid Honolulu--Sydney fish auction format, which combines English and Dutch features, are of interest.
4. Extent of Strategy-Proofness: The paper identifies trade-offs between shill-proofness and strategy-proofness. In the field of static or one-shot auctions, the researchers prove no auction can concurrently embody optimality, strategy-proofness, and weak shill-proofness. This results from inherent conflicts between incentivizing truthful bidding and preventing shill tactics.
5. Mechanism Design Beyond Ideal Settings: While the primary results center on public auctions, the paper contemplates setting-specific challenges where bidders have partial visibility into others' actions and where control of information is the auctioneer's prerogative.

Implications and Future Prospects

This research underscores the complexities of designing auctions resistant to seller manipulation, a necessary consideration for online and traditional auction platforms alike. It highlights how ensuring shill-proofness may necessitate concessions on strategy-proofness and efficiency, inviting avenues for further exploration regarding dynamic or complex auction settings, such as multi-item auctions or those involving common value elements.

By emphasizing the unique robustness of the Dutch auction format, this paper potentially guides designers in structuring systems to mitigate dishonest behaviors while also stressing the contextual limits of such defenses. Future inquiries could extend into algorithmic implementations that adaptively align with both seller and market risks or delve into auction applications in digital finance markets, where decentralized protocols may redefine transparency and participation reliability.

Overall, this paper offers a meticulous examination of auction robustness against shill tactics and sits at the intersection of economic theory, strategic interaction analysis, and computational design.