In non-truthful auctions, agents' utility for a strategy depends on the strategies of the opponents and also the prior distribution over their private types; the set of Bayes Nash equilibria generally has an intricate dependence on the prior. Using the First Price Auction as our main demonstrating example, we show that $\tilde O(n / ε^2)$ samples from the prior with $n$ agents suffice for an algorithm to learn the interim utilities for all monotone bidding strategies. As a consequence, this number of samples suffice for learning all approximate equilibria. We give almost matching (up to polylog factors) lower bound on the sample complexity for learning utilities. We also consider a setting where agents must pay a search cost to discover their own types. Drawing on a connection between this setting and the first price auction, discovered recently by Kleinberg et al. (2016), we show that $\tilde O(n / ε^2)$ samples suffice for utilities and equilibria to be estimated in a near welfare-optimal descending auction in this setting. En route, we improve the sample complexity bound, recently obtained by Guo et al. (2021), for the Pandora's Box problem, which is a classical model for sequential consumer search.
Learning to Coordinate Bidders in Non-Truthful Auctions
Shanghai University of Finance and Economics, School of Computing and Artificial Intelligence, Key Laboratory of Interdisciplinary Research of Computation and Economics（上海财经大学，计算机与人工智能学院，计算与经济学交叉研究重点实验室）；Microsoft Research & The Chinese University of Hong Kong, Shenzhen（微软研究院及香港中文大学（深圳））
We present a general framework for designing approximately revenue-optimal mechanisms for multi-item additive auctions, which applies to both truthful and non-truthful auctions. Given a (not necessarily truthful) single-item auction format $A$ satisfying certain technical conditions, we run simultaneous item auctions augmented with a personalized entry fee for each bidder that must be paid before the auction can be accessed. These entry fees depend only on the prior distribution of bidder types, and in particular are independent of realized bids. We bound the revenue of the resulting two-part …
Designing truthful, revenue maximizing auctions is a core problem of auction design. Multi-item settings have long been elusive. Recent work (arXiv:1706.03459) introduces effective deep learning techniques to find such auctions for the prior-dependent setting, in which distributions about bidder preferences are known. One remaining problem is to obtain priors in a way that excludes the possibility of manipulating the resulting auctions. Using techniques from differential privacy for the construction of approximately truthful mechanisms, we modify the RegretNet approach to be applicable to the …
Statistically Truthful Auctions via Acceptance Rule
Department of Electrical and Computer Engineering, Technion IIT, Israel（电气与计算机工程系，技术学院IIT，以色列）；Department of Computer Science, Technion IIT, Israel（计算机科学系，技术学院IIT，以色列）
Auto-bidding is now widely adopted as an interface between advertisers and internet advertising as it allows advertisers to specify high-level goals, such as maximizing value subject to a value-per-spend constraint. Prior research has mostly focused on auctions which are truthful (such as SPA) since uniform bidding is optimal in such auctions, which makes it manageable to reason about equilibria. A tantalizing question is whether one can obtain more efficient outcomes by leaving the realm of truthful auctions. This is the first paper to study non-truthful auctions in the prior-free auto-biddin…
In this paper, we study efficiency in truthful auctions via a social network, where a seller can only spread the information of an auction to the buyers through the buyers' network. In single-item auctions, we show that no mechanism is strategy-proof, individually rational, efficient, and weakly budget balanced. In addition, we propose $α$-APG mechanisms, a class of mechanisms which operate a trade-off between efficiency and weakly budget balancedness. In multi-item auctions, there already exists a strategy-proof mechanism when all buyers need only one item. However, we indicate a counter-exam…
One of the fundamental questions of Algorithmic Mechanism Design is whether there exists an inherent clash between truthfulness and computational tractability: in particular, whether polynomial-time truthful mechanisms for combinatorial auctions are provably weaker in terms of approximation ratio than non-truthful ones. This question was very recently answered for universally truthful mechanisms for combinatorial auctions \cite{D11}, and even for truthful-in-expectation mechanisms \cite{DughmiV11}. However, both of these results are based on information-theoretic arguments for valuations given…
Truthful spectrum auctions have been extensively studied in recent years. Truthfulness makes bidders bid their true valuations, simplifying greatly the analysis of auctions. However, revealing one's true valuation causes severe privacy disclosure to the auctioneer and other bidders. To make things worse, previous work on secure spectrum auctions does not provide adequate security. In this paper, based on TRUST, we propose PS-TRUST, a provably secure solution for truthful double spectrum auctions. Besides maintaining the properties of truthfulness and special spectrum reuse of TRUST, PS-TRUST a…
For sponsored search auctions, we consider contextual multi-armed bandit problem in the presence of strategic agents. In this setting, at each round, an advertising platform (center) runs an auction to select the best-suited ads relevant to the query posted by the user. It is in the best interest of the center to select an ad that has a high expected value (i.e., probability of getting a click $\times$ value it derives from a click of the ad). The probability of getting a click (CTR) is unknown to the center and depends on the user's profile (context) posting the query. Further, the value deri…
Redistribution mechanism design aims to redistribute the revenue collected by a truthful auction back to its participants without affecting the truthfulness. We study redistribution mechanisms for diffusion auctions, which is a new trend in mechanism design [19]. The key property of a diffusion auction is that the existing participants are incentivized to invite new participants to join the auctions. Hence, when we design redistributions, we also need to maintain this incentive. Existing redistribution mechanisms in the traditional setting are targeted at modifying the payment design of a trut…
In this paper, we study online double auctions, where multiple sellers and multiple buyers arrive and depart dynamically to exchange one commodity. We show that there is no deterministic online double auction that is truthful and competitive for maximising social welfare in an adversarial model. However, given the prior information that sellers are patient and the demand is not more than the supply, a deterministic and truthful greedy mechanism is actually 2-competitive, i.e. it guarantees that the social welfare of its allocation is at least half of the optimal one achievable offline. Moreove…
We provide the first separation in the approximation guarantee achievable by truthful and non-truthful combinatorial auctions with polynomial communication. Specifically, we prove that any truthful mechanism guaranteeing a $(\frac{3}{4}-\frac{1}{240}+\varepsilon)$-approximation for two buyers with XOS valuations over $m$ items requires $\exp(Ω(\varepsilon^2 \cdot m))$ communication, whereas a non-truthful algorithm by Dobzinski and Schapira [SODA 2006] and Feige [2009] is already known to achieve a $\frac{3}{4}$-approximation in $poly(m)$ communication. We obtain our separation by proving that…
We study the communication complexity of combinatorial auctions via interpolation mechanisms that interpolate between non-truthful and truthful protocols. Specifically, an interpolation mechanism has two phases. In the first phase, the bidders participate in some non-truthful protocol whose output is itself a truthful protocol. In the second phase, the bidders participate in the truthful protocol selected during phase one. Note that virtually all existing auctions have either a non-existent first phase (and are therefore truthful mechanisms), or a non-existent second phase (and are therefore j…
This manuscript presents an alternative implementation of the truthful-in-expectation mechanism of Dughmi, Roughgarden and Yan for combinatorial auctions with weighted-matroid-rank-sum valuations. The new implementation uses only value queries and is approximately truthful-in-expectation, in the sense that by reporting truthfully each agent maximizes his utility within a multiplicative 1-o(1) factor. It still provides an optimal (1-1/e-o(1))-approximation in social welfare. We achieve this by first presenting an approximately maximal-in-distributional-range allocation rule and then showing a b…
In a seminal paper, McAfee (1992) presented a truthful mechanism for double auctions, attaining asymptotically-optimal gain-from-trade without any prior information on the valuations of the traders. McAfee's mechanism handles single-parametric agents, allowing each seller to sell a single unit and each buyer to buy a single unit. This paper presents a double-auction mechanism that handles multi-parametric agents and allows multiple units per trader, as long as the valuation functions of all traders have decreasing marginal returns. The mechanism is prior-free, ex-post individually-rational, do…
We study a basic auction design problem with online supply. There are two unit-demand bidders and two types of items. The first item type will arrive first for sure, and the second item type may or may not arrive. The auctioneer has to decide the allocation of an item immediately after each item arrives, but is allowed to compute payments after knowing how many items arrived. For this problem we show that there is no deterministic truthful and individually rational mechanism that, even with unbounded computational resources, gets any finite approximation factor to the optimal social welfare.
Sponsored search auctions constitute one of the most successful applications of microeconomic mechanisms. In mechanism design, auctions are usually designed to incentivize advertisers to bid their truthful valuations and to assure both the advertisers and the auctioneer a non-negative utility. Nonetheless, in sponsored search auctions, the click-through-rates (CTRs) of the advertisers are often unknown to the auctioneer and thus standard truthful mechanisms cannot be directly applied and must be paired with an effective learning algorithm for the estimation of the CTRs. This introduces the cri…
We study truthful mechanisms for hiring a team of agents in three classes of set systems: Vertex Cover auctions, k-flow auctions, and cut auctions. For Vertex Cover auctions, the vertices are owned by selfish and rational agents, and the auctioneer wants to purchase a vertex cover from them. For k-flow auctions, the edges are owned by the agents, and the auctioneer wants to purchase k edge-disjoint s-t paths, for given s and t. In the same setting, for cut auctions, the auctioneer wants to purchase an s-t cut. Only the agents know their costs, and the auctioneer needs to select a feasible set …
In markets such as digital advertising auctions, bidders want to maximize value rather than payoff. This is different to the utility functions typically assumed in auction theory and leads to different strategies and outcomes. We refer to bidders who maximize value as value bidders. While simple single-object auction formats are truthful, standard multi-object auction formats allow for manipulation. It is straightforward to show that there cannot be a truthful and revenue-maximizing deterministic auction mechanism with value bidders and general valuations. Approximation has been used as a mean…
We show that every universally truthful randomized mechanism for combinatorial auctions with submodular valuations that provides $m^{\frac 1 2 -ε}$ approximation to the social welfare and uses value queries only must use exponentially many value queries, where $m$ is the number of items. In contrast, ignoring incentives there exist constant ratio approximation algorithms for this problem. Our approach is based on a novel \emph{direct hardness} approach and completely skips the notoriously hard characterization step. The characterization step was the main obstacle for proving impossibility resu…
The difference set of an outcome in an auction is the set of types that the auction mechanism maps to the outcome. We give a complete characterization of the geometry of the difference sets that can appear for a dominant strategy incentive compatible multi-unit auction showing that they correspond to regular subdivisions of the unit cube. This observation is then used to construct mechanisms that are robust in the sense that the set of items allocated to a player does change only slightly when the player's reported type is changed slightly.
Online double auctions (DAs) model a dynamic two-sided matching problem with private information and self-interest, and are relevant for dynamic resource and task allocation problems. We present a general method to design truthful DAs, such that no agent can benefit from misreporting its arrival time, duration, or value. The family of DAs is parameterized by a pricing rule, and includes a generalization of McAfee's truthful DA to this dynamic setting. We present an empirical study, in which we study the allocative-surplus and agent surplus for a number of different DAs. Our results illustrate …
We present a computationally-efficient truthful mechanism for combinatorial auctions with subadditive bidders that achieves an $O((\log\!\log{m})^3)$-approximation to the maximum welfare in expectation using $O(n)$ demand queries; here $m$ and $n$ are the number of items and bidders, respectively. This breaks the longstanding logarithmic barrier for the problem dating back to the $O(\log{m}\cdot\log\!\log{m})$-approximation mechanism of Dobzinski from 2007. Along the way, we also improve and considerably simplify the state-of-the-art mechanisms for submodular bidders.
Korea University（高丽大学）；Hallym University（翰林大学）；California State University, Long Beach（加州州立大学长滩分校）
A successful deployment of drones provides an ideal solution for surveillance systems. Using drones for surveillance can provide access to areas that may be difficult or impossible to reach by humans or in-land vehicles gathering images or video recordings of a specific target in their coverage. Therefore, we introduces a data delivery drone to transfer collected surveillance data in harsh communication conditions. This paper proposes a Myerson auction-based asynchronous data delivery in an aerial distributed data platform in surveillance systems taking battery limitation and long flight const…
With the increasing use of auctions in online advertising, there has been a large effort to study seller revenue maximization, following Myerson's seminal work, both theoretically and practically. We take the point of view of the buyer in classical auctions and ask the question of whether she has an incentive to shade her bid even in auctions that are reputed to be truthful, when aware of the revenue optimization mechanism. We show that in auctions such as the Myerson auction or a VCG with reserve price set as the monopoly price, the buyer who is aware of this information has indeed an incenti…
We design a framework for truthful double multi-channel spectrum auctions where each seller (or buyer) can sell (or buy) multiple spectrum channels based on their individual needs. Open, market-based spectrum trading motivates existing spectrum owners (as sellers) to lease their selected idle spectrum channels to new spectrum users (as buyers) who need the spectrum desperately. The most significant requirement is how to make the auction economic-robust (truthful in particular) while enabling spectrum reuse to improve spectrum utilization. Additionally, in practice, both sellers and buyers woul…
Secondary spectrum auction is widely applied in wireless networks for mitigating the spectrum scarcity. In a realistic spectrum trading market, the requests from secondary users often specify the usage of a fixed spectrum frequency band in a certain geographical region and require a duration time in a fixed available time interval. Considering the selfish behaviors of secondary users, it is imperative to design a truthful auction which matches the available spectrums and requests of secondary users optimally. Unfortunately, existing designs either do not consider spectrum heterogeneity or igno…
A longstanding open problem in Algorithmic Mechanism Design is to design computationally-efficient truthful mechanisms for (approximately) maximizing welfare in combinatorial auctions with submodular bidders. The first such mechanism was obtained by Dobzinski, Nisan, and Schapira [STOC'06] who gave an $O(\log^2{m})$-approximation where $m$ is the number of items. This problem has been studied extensively since, culminating in an $O(\sqrt{\log{m}})$-approximation mechanism by Dobzinski [STOC'16]. We present a computationally-efficient truthful mechanism with approximation ratio that improves up…
In this paper we present and evaluate a general framework for the design of truthful auctions for matching agents in a dynamic, two-sided market. A single commodity, such as a resource or a task, is bought and sold by multiple buyers and sellers that arrive and depart over time. Our algorithm, Chain, provides the first framework that allows a truthful dynamic double auction (DA) to be constructed from a truthful, single-period (i.e. static) double-auction rule. The pricing and matching method of the Chain construction is unique amongst dynamic-auction rules that adopt the same building block. …
In most of microeconomic theory, consumers are assumed to exhibit decreasing marginal utilities. This paper considers combinatorial auctions among such submodular buyers. The valuations of such buyers are placed within a hierarchy of valuations that exhibit no complementarities, a hierarchy that includes also OR and XOR combinations of singleton valuations, and valuations satisfying the gross substitutes property. Those last valuations are shown to form a zero-measure subset of the submodular valuations that have positive measure. While we show that the allocation problem among submodular valu…
Interdependent values make basic auction design tasks -- in particular maximizing welfare truthfully in single-item auctions -- quite challenging. Eden et al. recently established that if the bidders valuation functions are submodular over their signals (a.k.a. SOS), a truthful 4-approximation to the optimal welfare exists. We show existence of a mechanism that is truthful and achieves a tight 2-approximation to the optimal welfare when signals are binary. Our mechanism is randomized and assigns bidders only 0 or 0.5 probabilities of winning the item. Our results utilize properties of submodul…
Recently, a randomized mechanism has been discovered [Dughmi, Roughgarden and Yan; STOC'11] for combinatorial auctions that is truthful in expectation and guarantees a (1-1/e)-approximation to the optimal social welfare when players have coverage valuations. This approximation ratio is the best possible even for non-truthful algorithms, assuming $P \neq NP$. Given the recent sequence of negative results for combinatorial auctions under more restrictive notions of incentive compatibility, this development raises a natural question: Are truthful-in-expectation mechanisms compatible with polynomi…
In this work, we investigate online mechanisms for trading time-sensitive valued data. We adopt a continuous function $d(t)$ to represent the data value fluctuation over time $t$. Our objective is to design an \emph{online} mechanism achieving \emph{truthfulness} and \emph{revenue-competitiveness}. We first prove several lower bounds on the revenue competitive ratios under various assumptions. We then propose several online truthful auction mechanisms for various adversarial models, such as a randomized observe-then-select mechanism $\mathcal{M}_1$ and prove that it is \textit{truthful} and $Θ…
One significant challenge in cognitive radio networks is to design a framework in which the selfish secondary users are obliged to interact with each other truthfully. Moreover, due to the vulnerability of these networks against jamming attacks, designing anti-jamming defense mechanisms is equally important. %providing the security defense is also of great importance. In this paper, we propose a truthful mechanism, robust against the jamming, for a dynamic stochastic cognitive radio network consisting of several selfish secondary users and a malicious user. In this model, each secondary user p…
We consider the problem of designing a revenue-maximizing auction for a single item, when the values of the bidders are drawn from a correlated distribution. We observe that there exists an algorithm that finds the optimal randomized mechanism that runs in time polynomial in the size of the support. We leverage this result to show that in the oracle model introduced by Ronen and Saberi [FOCS'02], there exists a polynomial time truthful in expectation mechanism that provides a $(\frac 3 2+ε)$-approximation to the revenue achievable by an optimal truthful-in-expectation mechanism, and a polynomi…
This paper studies a mechanism design problem over a network, where agents can only participate by referrals. The Bulow-Klemberer theorem proposes that expanding the number of participants is a more effective approach to increase revenue than modifying the auction format. However, agents lack the motivation to invite others because doing so intensifies competition among them. On the other hand, misreporting social networks is also a common problem that can reduce revenue. Examples of misreporting include Sybil attacks (an agent pretending to be multiple bidders) and coalition groups (multiple …
In this work, we study spectrum auction problem where each request from secondary users has spatial, temporal, and spectral features. With the requests of secondary users and the reserve price of the primary user, our goal is to design truthful mechanisms that will either maximize the social efficiency or maximize the revenue of the primary user. As the optimal conflict-free spectrum allocation problem is NP-hard, in this work, we design near optimal spectrum allocation mechanisms separately based on the following techniques: derandomized allocation from integer programming formulation, its li…
As cellular operators are suffering from a data explosion problem, and users are consequently experiencing poor data services, the introduction of femtocells offers a cost-effective way to mitigate this problem. Femtocells enable larger network capacity by increasing spatial reuse of the spectrum and shortening the distance to the users. Existing work has shown that open access femtocells, which allow unregistered macro users to connect, are efficient in reducing inter-cell interference and offloading traffic. However, a major obstacle constraining the potential capability of femtocells and op…
We study incentive compatible mechanisms for Combinatorial Auctions where the bidders have submodular (or XOS) valuations and are budget-constrained. Our objective is to maximize the \emph{liquid welfare}, a notion of efficiency for budget-constrained bidders introduced by Dobzinski and Paes Leme (2014). We show that some of the known truthful mechanisms that best-approximate the social welfare for Combinatorial Auctions with submodular bidders through demand query oracles can be adapted, so that they retain truthfulness and achieve asymptotically the same approximation guarantees for the liqu…
We present algorithms for implementing local spectrum redistribution in wireless networks using a mechanism design approach. For example, in single-hop request scheduling, secondary users are modeled as rational agents that have private utility when getting assigned a channel for successful transmission. We present a rather simple algorithmic technique that allows to turn existing and future approximation algorithms and heuristics into truthful mechanisms for a large variety of networking problems. In contrast to previous work, our approach works for virtually all known interference models in …
Device-to-Device communication allows a cellular user (relay node) to relay data between the base station (BS) and another cellular user (destination node). We address the problem of designing reverse auctions to assign a relay node to each destination node, when there are multiple potential relay nodes and multiple destination nodes, in the scenarios where the transmission powers of the relay nodes are: 1) fixed, 2) selected to achieve the data rates desired by destination nodes, and 3) selected so as to approximately maximize the BS's utility. We show that auctions based on the widely used V…
In the standard single-dimensional model of position auctions, bidders agree on the relative values of the positions and each of them submits a single bid that is interpreted in terms of these values. Motivated by current practice in sponsored search we consider a situation where the auctioneer uses estimates of the relative values, which may be imprecise, and show that under both complete and incomplete information a non-truthful mechanism is able to support an efficient outcome in equilibrium for a wider range of these estimates than the VCG mechanism. We thus exhibit a property of the VCG m…
We study a central problem in Algorithmic Mechanism Design: constructing truthful mechanisms for welfare maximization in combinatorial auctions with submodular bidders. Dobzinski, Nisan, and Schapira provided the first mechanism that guarantees a non-trivial approximation ratio of $O(\log^2 m)$ [STOC'06], where $m$ is the number of items. This was subsequently improved to $O(\log m\log \log m)$ [Dobzinski, APPROX'07] and then to $O(\log m)$ [Krysta and Vocking, ICALP'12]. In this paper we develop the first mechanism that breaks the logarithmic barrier. Specifically, the mechanism provides an a…
We study online auction settings in which agents arrive and depart dynamically in a random (secretary) order, and each agent's private type consists of the agent's arrival and departure times, value and budget. We consider multi-unit auctions with additive agents for the allocation of both divisible and indivisible items. For both settings, we devise truthful mechanisms that give a constant approximation with respect to the auctioneer's revenue, under a large market assumption. For divisible items, we devise in addition a truthful mechanism that gives a constant approximation with respect to t…
First-price auctions have many desirable properties, including uniquely possessing some, like credibility. However, first-price auctions are also inherently non-truthful, and non-truthfulness may result in instability and inefficiencies. Given these pros and cons, we seek to quantify the extent to which first-price auctions are susceptible to manipulation. In this work we adopt a metric that was introduced in the context of bitcoin fee design markets: the percentage change in payment that can be achieved by being strategic. We study the behavior of this metric for single-unit and $k$-unit auct…
Algorithmic mechanism design (AMD) studies the delicate interplay between computational efficiency, truthfulness, and optimality. We focus on AMD's paradigmatic problem: combinatorial auctions. We present a new generalization of the VC dimension to multivalued collections of functions, which encompasses the classical VC dimension, Natarajan dimension, and Steele dimension. We present a corresponding generalization of the Sauer-Shelah Lemma and harness this VC machinery to establish inapproximability results for deterministic truthful mechanisms. Our results essentially unify all inapproximabil…
University of Bremen（不来梅大学）；ISL - Institute of Shipping Economics and Logistics（ISL——航运经济与物流研究所）
To support a freight carrier in a combinatorial transport auction, we proposes an exact and two heuristic strategies for bidding on subsets of requests. The exact bidding strategy is based on the concept of elementary request combinations. We show that it is sufficient and necessary for a carrier to bid on each elementary request combination in order to guarantee the same result as bidding on each element of the powerset of the set of tendered requests. Both heuristic bidding strategies identify promising request combinations. For this, pairwise synergies based on saving values as well as the …
