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1. On the hardness of dominant strategy mechanism design

   https://doi.org/10.1145/3519935.3520013  

   Dobzinski, Shahar; Ron, Shiri; Vondrák, Jan (June 2022, STOC 2022: Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing)

   Stefano Leonardi (Ed.)

   We study the communication complexity of dominant strategy implementations of combinatorial auctions. We start with two domains that are generally considered “easy”: multi-unit auctions with decreasing marginal values and combinatorial auctions with gross substitutes valuations. For both domains we have fast algorithms that find the welfare-maximizing allocation with communication complexity that is poly-logarithmic in the input size. This immediately implies that welfare maximization can be achieved in ex-post equilibrium with no significant communication cost, by using VCG payments. In contrast, we show that in both domains the communication complexity of any dominant strategy implementation that achieves the optimal welfare is polynomial in the input size. We then move on to studying the approximation ratios achievable by dominant strategy mechanisms. For multi-unit auctions with decreasing marginal values, we provide a dominant-strategy communication FPTAS. For combinatorial auctions with general valuations, we show that there is no dominant strategy mechanism that achieves an approximation ratio better than m1−є that uses poly(m,n) bits of communication, where m is the number of items and n is the number of bidders. In contrast, a randomized dominant strategy mechanism that achieves an O(√m) approximation with poly(m,n) communication is known. This proves the first gap between computationally efficient deterministic dominant strategy mechanisms and randomized ones. En route, we answer an open question on the communication cost of implementing dominant strategy mechanisms for more than two players, and also solve some open problems in the area of simultaneous combinatorial auctions. 

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2. Optimal Deterministic Clock Auctions and Beyond

   Christodoulou, Giorgos; Gkatzelis, Vasilis; Schoepflin, Daniel (February 2022, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022))

   We design and analyze deterministic and randomized clock auctions for single-parameter domains with downward-closed feasibility constraints, aiming to maximize the social welfare. Clock auctions have been shown to satisfy a list of compelling incentive properties making them a very practical solution for real-world applications, partly because they require very little reasoning from the participating bidders. However, the first results regarding the worst-case performance of deterministic clock auctions from a welfare maximization perspective indicated that they face obstacles even for a seemingly very simple family of instances, leading to a logarithmic inapproximability result; this inapproximability result is information-theoretic and holds even if the auction has unbounded computational power. In this paper we propose a deterministic clock auction that achieves a logarithmic approximation for any downward-closed set system, using black box access to a solver for the underlying optimization problem. This proves that our clock auction is optimal and that the aforementioned family of instances exactly captures the information limitations of deterministic clock auctions. We then move beyond deterministic auctions and design randomized clock auctions that achieve improved approximation guarantees for a generalization of this family of instances, suggesting that the earlier indications regarding the performance of clock auctions may have been overly pessimistic. 

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3. Calibrated Click-Through Auctions

   https://doi.org/10.1145/3485447.3512050  

   Bergemann, Dirk; Dütting, Paul; Paes Leme, Renato; Zuo, Song (April 2022, ACM Web Conference)

   We analyze the optimal information design in a click-through auction with stochastic click-through rates and known valuations per click. The auctioneer takes as given the auction rule of the clickthrough auction, namely the generalized second-price auction. Yet, the auctioneer can design the information flow regarding the clickthrough rates among the bidders. We require that the information structure to be calibrated in the learning sense. With this constraint, the auction needs to rank the ads by a product of the value and a calibrated prediction of the click-through rates. The task of designing an optimal information structure is thus reduced to the task of designing an optimal calibrated prediction. We show that in a symmetric setting with uncertainty about the click-through rates, the optimal information structure attains both social efficiency and surplus extraction. The optimal information structure requires private (rather than public) signals to the bidders. It also requires correlated (rather than independent) signals, even when the underlying uncertainty regarding the click-through rates is independent. Beyond symmetric settings, we show that the optimal information structure requires partial information disclosure, and achieves only partial surplus extraction. 

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4. When Bidders Are DAOs

   https://doi.org/10.4230/LIPIcs.AFT.2023.21  

   Bahrani, Maryam; Garimidi, Pranav; Roughgarden, Tim (January 2023, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)

   Bonneau, Joseph; Weinberg, S Matthew (Ed.)

   In a typical decentralized autonomous organization (DAO), people organize themselves into a group that is programmatically managed. DAOs can act as bidders in auctions (with ConstitutionDAO being one notable example), with a DAO’s bid typically treated by the auctioneer as if it had been submitted by an individual, without regard to any details of the internal DAO dynamics. The goal of this paper is to study auctions in which the bidders are DAOs. More precisely, we consider the design of two-level auctions in which the "participants" are groups of bidders rather than individuals. Bidders form DAOs to pool resources, but must then also negotiate the terms by which the DAO’s winnings are shared. We model the outcome of a DAO’s negotiations through an aggregation function (which aggregates DAO members' bids into a single group bid) and a budget-balanced cost-sharing mechanism (that determines DAO members' access to the DAO’s allocation and distributes the aggregate payment demanded from the DAO to its members). DAOs' bids are processed by a direct-revelation mechanism that has no knowledge of the DAO structure (and thus treats each DAO as an individual). Within this framework, we pursue two-level mechanisms that are incentive-compatible (with truthful bidding a dominant strategy for each member of each DAO) and approximately welfare-optimal. We prove that, even in the case of a single-item auction, the DAO dynamics hidden from the outer mechanism preclude incentive-compatible welfare maximization: No matter what the outer mechanism and the cost-sharing mechanisms used by DAOs, the welfare of the resulting two-level mechanism can be a ≈ ln n factor less than the optimal welfare (in the worst case over DAOs and valuation profiles). We complement this lower bound with a natural two-level mechanism that achieves a matching approximate welfare guarantee. This upper bound also extends to multi-item auctions in which individuals have additive valuations. Finally, we show that our positive results cannot be extended much further: Even in multi-item settings in which bidders have unit-demand valuations, truthful two-level mechanisms form a highly restricted class and as a consequence cannot guarantee any non-trivial approximation of the maximum social welfare. 

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5. Clock Auctions Augmented with Unreliable Advice

   Gkatzelis, Vasilis; Schoepflin, Daniel; Tan, Xizhi (January 2025, Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms,(SODA 2025))

   Azar, Yossi; Panigrahi, Debmalya (Ed.)

   We provide the first analysis of (deferred acceptance) clock auctions in the learning-augmented framework. These auctions satisfy a unique list of very appealing properties, including obvious strategyproofness, transparency, and unconditional winner privacy, making them particularly well-suited for real-world applications. However, early work that evaluated their performance from a worst-case analysis perspective concluded that no deterministic clock auction with n bidders can achieve a O (log1-∈ n ) approximation of the optimal social welfare for a constant ∈ > 0, even in very simple settings. This overly pessimistic impossibility result heavily depends on the assumption that the designer has no information regarding the bidders’ values. Leveraging the learning-augmented framework, we instead consider a designer equipped with some (machine-learned) advice regarding the optimal solution; this advice can provide useful guidance if accurate, but it may be unreliable. Our main results are learning-augmented clock auctions that use this advice to achieve much stronger performance guarantees whenever the advice is accurate (known as consistency), while maintaining worst-case guarantees even if this advice is arbitrarily inaccurate (known as robustness ). Our first clock auction achieves the best of both worlds: (1 + ∈ )-consistency for any desired constant ∈ > 0 and O (log n ) robustness; we also extend this auction to achieve error tolerance. We then consider a much stronger notion of consistency, which we refer to as consistency∞ and provide an auction that achieves a near-optimal trade-off between consistency∞ and robustness. Finally, using our impossibility results regarding this trade-off, we prove lower bounds on the “cost of smoothness,” i.e., on the robustness that is achievable if we also require that the performance of the auction degrades smoothly as a function of the prediction error. 

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