We consider an auction design problem where a seller sells multiple homogeneous items to a set of connected buyers. Each buyer only knows the buyers she directly connects with and has a diminishing marginal utility valuation for the items. The seller initially only connects to some buyers who can be directly invited to the sale by the seller. Our goal is to design an auction to incentivize the buyers who are aware of the auction to further invite their neighbors to join the auction. This is challenging because the buyers are competing for the items and they would not invite each other by default. Thus, rewards need to be given to buyers who diffuse information, but the rewards should be carefully designed to guarantee both invitation incentives and the seller's revenue. Solutions have been proposed recently for the settings where each buyer requires at most one unit and demonstrated the difficulties of the design. We move this forward to propose the very first diffusion auction for the multi-unit demand settings to improve both the social welfare and the seller's revenue.
We study the problem of characterizing revenue optimal auctions for single-minded buyers. Each buyer is interested only in a specific bundle of items and has a value for the same. Both his bundle and its value are his private information. The bundles that buyers are interested in and their corresponding values are assumed to be realized from known probability distributions independent across the buyers. We identify revenue optimal auctions with a simple structure, if the conditional distribution of any buyer's valuation is nondecreasing, in the hazard rates ordering of probability distribution…
We study dynamic mechanisms for optimizing revenue in repeated auctions, that are robust to heterogeneous forward-looking and learning behavior of the buyers. Typically it is assumed that the buyers are either all myopic or are all infinite lookahead, and that buyers understand and trust the mechanism. These assumptions raise the following question: is it possible to design approximately revenue optimal mechanisms when the buyer pool is heterogeneous? Facing a heterogeneous population of buyers with an unknown mixture of $k$-lookahead buyers, myopic buyers, no-regret-learners and no-policy-reg…
We study the efficiency of sequential multiunit auctions with two-buyers and complete information. For general valuation functions, we show that the price of anarchy is exactly $1/T$ for auctions with $T$ items for sale. For concave valuation functions, we show that the price of anarchy is bounded below by $1-1/e\simeq 0.632$. This bound is asymptotically tight as the number of items sold tends to infinity.
We study revenue optimization in a repeated auction between a single seller and a single buyer. Traditionally, the design of repeated auctions requires strong modeling assumptions about the bidder behavior, such as it being myopic, infinite lookahead, or some specific form of learning behavior. Is it possible to design mechanisms which are simultaneously optimal against a multitude of possible buyer behaviors? We answer this question by designing a simple state-based mechanism that is simultaneously approximately optimal against a $k$-lookahead buyer for all $k$, a buyer who is a no-regret lea…
We study efficiency loss in Bayesian revenue optimal auctions. We quantify this as the worst case ratio of loss in the realized social welfare to the social welfare that can be realized by an efficient auction. Our focus is on auctions with single-parameter buyers and where buyers' valuation sets are finite. For binary valued single-parameter buyers with independent (not necessarily identically distributed) private valuations, we show that the worst case efficiency loss ratio (ELR) is no worse than it is with only one buyer; moreover, it is at most 1/2. Moving beyond the case of binary valuati…
We study equilibria in two-buyer sequential second-price (or first-price) auctions for identical goods. Buyers have weakly decreasing incremental values, and we make a behavioural no-overbidding assumption: the buyers do not bid above their incremental values. Structurally, we show equilibria are intrinsically linked to a greedy bidding strategy. We then prove three results. First, any equilibrium consists of three phases: a competitive phase, a competition reduction phase and a monopsony phase. In particular, there is a time after which one buyer exhibits monopsonistic behaviours. Second, the…
We consider a monopoly seller who optimally auctions a single object to a single potential buyer, with a known distribution of valuations. We show that a tight lower bound on the seller's expected revenue is $1/e$ times the geometric expectation of the buyer's valuation, and that this bound is uniquely achieved for the equal revenue distribution. We show also that when the valuation's expectation and geometric expectation are close, then the seller's expected revenue is close to the expected valuation.
This letter considers the design of an auction mechanism to sell the object of a seller when the buyers quantize their private value estimates regarding the object prior to communicating them to the seller. The designed auction mechanism maximizes the utility of the seller (i.e., the auction is optimal), prevents buyers from communicating falsified quantized bids (i.e., the auction is incentive-compatible), and ensures that buyers will participate in the auction (i.e., the auction is individually-rational). The letter also investigates the design of the optimal quantization thresholds using wh…
Crémer and McLean [1985] showed that, when buyers' valuations are drawn from a correlated distribution, an auction with full knowledge on the distribution can extract the full social surplus. We study whether this phenomenon persists when the auctioneer has only incomplete knowledge of the distribution, represented by a finite family of candidate distributions, and has sample access to the real distribution. We show that the naive approach which uses samples to distinguish candidate distributions may fail, whereas an extended version of the Crémer-McLean auction simultaneously extracts full so…
For Bayesian combinatorial auctions, we present a general framework for approximately reducing the mechanism design problem for multiple buyers to single buyer sub-problems. Our framework can be applied to any setting which roughly satisfies the following assumptions: (i) buyers' types must be distributed independently (not necessarily identically), (ii) objective function must be linearly separable over the buyers, and (iii) except for the supply constraints, there should be no other inter-buyer constraints. Our framework is general in the sense that it makes no explicit assumption about buye…
We consider the practical and classical setting where the seller is using an exploration stage to learn the value distributions of the bidders before running a revenue-maximizing auction in a exploitation phase. In this two-stage process, we exhibit practical, simple and robust strategies with large utility uplifts for the bidders. We quantify precisely the seller revenue against non-discounted buyers, complementing recent studies that had focused on impatient/heavily discounted buyers. We also prove the robustness of these shading strategies to sample approximation error of the seller, to bid…
In this paper, we introduce a Bayesian revenue-maximizing mechanism design model where the items have fixed, exogenously-given prices. Buyers are unit-demand and have an ordinal ranking over purchasing either one of these items at its given price, or purchasing nothing. This model arises naturally from the assortment optimization problem, in that the single-buyer optimization problem over deterministic mechanisms reduces to deciding on an assortment of items to "show". We study its multi-buyer generalization in the simplest setting of single-winner auctions, or more broadly, any service-constr…
In digital goods auctions, there is an auctioneer who sells an item with unlimited supply to a set of potential buyers, and the objective is to design truthful auction to maximize the total profit of the auctioneer. Motivated from an observation that the values of buyers for the item could be interconnected through social networks, we study digital goods auctions with positive externalities among the buyers. This defines a multi-parameter auction design problem where the private valuation of every buyer is a function of other winning buyers. The main contribution of this paper is a truthful co…
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…
Recent spectrum auctions in the United Kingdom, and some proposals for future auctions of spectrum in the United States, are based on preliminary price discovery rounds, followed by calculation of final prices for the winning buyers. For example, the prices could be the projection of Vikrey prices onto the core of reported prices. The use of Vikrey prices should lead to more straightforward bidding, but the projection reverses some of the incentive for bidders to report truthfully. Still, we conjecture that the price paid by a winning buyer increases no faster than the bid, as in a first price…
The Competition Complexity of an auction measures how much competition is needed for the revenue of a simple auction to surpass the optimal revenue. A classic result from auction theory by Bulow and Klemperer [9], states that the Competition Complexity of VCG, in the case of n i.i.d. buyers and a single item, is 1, i.e., it is better to recruit one extra buyer and run a second price auction than to learn exactly the buyers' underlying distribution and run the revenue-maximizing auction tailored to this distribution. In this paper we study the Competition Complexity of dynamic auctions. Conside…
We study the design of truthful auctions for selling identical items in unlimited supply (e.g., digital goods) to n unit demand buyers. This classic problem stands out from profit-maximizing auction design literature as it requires no probabilistic assumptions on buyers' valuations and employs the framework of competitive analysis. Our objective is to optimize the worst-case performance of an auction, measured by the ratio between a given benchmark and revenue generated by the auction. We establish a sufficient and necessary condition that characterizes competitive ratios for all monotone benc…
A double auction game with an infinite number of buyers and sellers is introduced. All sellers posses one unit of a good, all buyers desire to buy one unit. Each seller and each buyer has a private valuation of the good. The distribution of the valuations define supply and demand functions. One unit of the good is auctioned. At successive, discrete time instances, a player is randomly selected to make a bid (buyer) or an ask (seller). When the maximum of the bids becomes larger than the minimum of the asks, a transaction occurs and the auction is closed. The players have to choose the value of…
Diffusion auction refers to an emerging paradigm of online marketplace where an auctioneer utilises a social network to attract potential buyers. Diffusion auction poses significant privacy risks. From the auction outcome, it is possible to infer hidden, and potentially sensitive, preferences of buyers. To mitigate such risks, we initiate the study of differential privacy (DP) in diffusion auction mechanisms. DP is a well-established notion of privacy that protects a system against inference attacks. Achieving DP in diffusion auctions is non-trivial as the well-designed auction rules are requi…
In a single-parameter mechanism design problem, a provider is looking to sell a service to a group of potential buyers. Each buyer $i$ has a private value $v_i$ for receiving the service and a feasibility constraint restricts which sets of buyers can be served simultaneously. Recent work in economics introduced clock auctions as a superior class of auctions for this problem, due to their transparency, simplicity, and strong incentive guarantees. Subsequent work focused on evaluating the social welfare approximation guarantees of these auctions, leading to strong impossibility results: in the a…
Consider the problem of allocating goods to buyers through an auction. An auction is efficient if the resulting allocation maximizes total welfare, conditional on the information available. If buyers have private values, the Vickrey-Groves-Clarke mechanism is efficient. If buyers have common values and a buyer's information can be summarized as a one-dimensional signal, Dasgupta and Maskin present an efficient auction. We construct an efficient auction mechanism in case buyer information is multidimensional, for a restricted class of valuation functions, and we prove which of the assumptions m…
We study the problem of selling a resource through an auction mechanism. The winning buyer in turn develops this resource to generate profit. Two forms of payment are considered: charging the winning buyer a one-time payment, or an initial payment plus a profit sharing contract (PSC). We consider a symmetric interdependent values model with risk averse or risk neutral buyers and a risk neutral seller. For the second price auction and the English auction, we show that the seller's expected total revenue from the auction where he also takes a fraction of the positive profit is higher than the ex…
We study the limits of an information intermediary in the classical Bayesian auction, where a revenue-maximizing seller sells one item to $n$ buyers with independent private values. In addition, we have an intermediary who knows the buyers' private values, and can map these to a public signal so as to increase consumer surplus. This model generalizes the single-buyer setting proposed by Bergemann, Brooks, and Morris, who present a signaling scheme that raises the optimal consumer surplus, by guaranteeing that the item is always sold and the seller gets the same revenue as without signaling. Ou…
One of the most celebrated results in mechanism design is Myerson's characterization of the revenue optimal auction for selling a single item. However, this result relies heavily on the assumption that buyers are indifferent to risk. In this paper we investigate the case where the buyers are risk-loving, i.e. they prefer gambling to being rewarded deterministically. We use the standard model for risk from expected utility theory, where risk-loving behavior is represented by a convex utility function. We focus our attention on the special case of exponential utility functions. We characterize t…
We study a classical Bayesian mechanism design problem where a seller is selling multiple items to multiple buyers. We consider the case where the seller has costs to produce the items, and these costs are private information to the seller. How can the seller design a mechanism to maximize her profit? Two well-studied problems, revenue maximization in multi-item auctions and signaling in ad auctions, are special cases of our problem. We show that there exists a simple mechanism whose profit is at least $\frac{1}{44}$ of the optimal profit for multiple buyers with matroid-rank valuation functio…
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 consider the revenue maximization problem of a monopolist via a non-Myersonian approach that could generalize to multiple items and multiple buyers. Although such an approach does not lead to any closed-form solution of the problem, it does provide some insights into this problem from different angles. In particular, we consider both Bayesian (Bayesian Incentive Compatible + Bayesian Individually Rational) and Dominant-Strategy (Dominant-Strategy Incentive Compatible + ex-post Individually Rational) implementations, where all the buyers have additive valuations and quasi-linear utilities an…
A Lookahead Auction (LA), introduced by Ronen, is an auction format for the sale of a single item among multiple buyers, which is considered simpler and more fair than the optimal auction. Indeed, it anonymously selects a provisional winner by a symmetric ascending-price process, and only then uses a personalized posted price. A LA auction extracts at least 1/2 of the optimal revenue, even under a correlated value distribution. This bound is tight, even for 2 buyers with independent values. We introduce a natural extension of LA, called lookahead with pooling (LAP). A LAP auction proceeds as L…
On ad exchange platforms the place for advertisement is sold through different kinds of auctions. However, it is not uncommon the situation where the seller repeatedly encounters only one buyer, thus the posted price auction degenerates into a monopoly-monopsony game with asymmetric information and nearly an infinite number of rounds; on each round the seller proposes the price and the buyer accepts or rejects it. I learned this problem from a discussion with members of Yandex research team and my main motivation was to find an incentive-compatible seller's strategy. In this short paper such a…
University of Pennsylvania（宾夕法尼亚大学）；Google Research（谷歌研究院）
Inspired by real-time ad exchanges for online display advertising, we consider the problem of inferring a buyer's value distribution for a good when the buyer is repeatedly interacting with a seller through a posted-price mechanism. We model the buyer as a strategic agent, whose goal is to maximize her long-term surplus, and we are interested in mechanisms that maximize the seller's long-term revenue. We define the natural notion of strategic regret --- the lost revenue as measured against a truthful (non-strategic) buyer. We present seller algorithms that are no-(strategic)-regret when the bu…
We study revenue optimization pricing algorithms for repeated posted-price auctions where a seller interacts with a single strategic buyer that holds a fixed private valuation. We show that, in the case when both the seller and the buyer have the same discounting in their cumulative utilities (revenue and surplus), there exist two optimal algorithms. The first one constantly offers the Myerson price, while the second pricing proposes a "big deal": pay for all goods in advance (at the first round) or get nothing. However, when there is an imbalance between the seller and the buyer in the patien…
We show that the multiplicative weight update method provides a simple recipe for designing and analyzing optimal Bayesian Incentive Compatible (BIC) auctions, and reduces the time complexity of the problem to pseudo-polynomial in parameters that depend on single agent instead of depending on the size of the joint type space. We use this framework to design computationally efficient optimal auctions that satisfy ex-post Individual Rationality in the presence of constraints such as (hard, private) budgets and envy-freeness. We also design optimal auctions when buyers and a seller's utility func…
This paper studies an auction design problem for a seller to sell a commodity in a social network, where each individual (the seller or a buyer) can only communicate with her neighbors. The challenge to the seller is to design a mechanism to incentivize the buyers, who are aware of the auction, to further propagate the information to their neighbors so that more buyers will participate in the auction and hence, the seller will be able to make a higher revenue. We propose a novel auction mechanism, called information diffusion mechanism (IDM), which incentivizes the buyers to not only truthfull…
The declining price anomaly states that the price weakly decreases when multiple copies of an item are sold sequentially over time. The anomaly has been observed in a plethora of practical applications. On the theoretical side, Gale and Stegeman proved that the anomaly is guaranteed to hold in full information sequential auctions with exactly two buyers. We prove that the declining price anomaly is not guaranteed in full information sequential auctions with three or more buyers. This result applies to both first-price and second-price sequential auctions. Moreover, it applies regardless of the…
In a second-price auction with i.i.d. (independent identically distributed) bidder valuations, adding bidders increases expected buyer surplus if the distribution of valuations has a sufficiently heavy right tail. While this does not imply that a bidder in an auction should prefer for more bidders to join the auction, it does imply that a bidder should prefer it in exchange for the bidder being allowed to participate in more auctions. Also, for a heavy-tailed valuation distribution, marginal expected seller revenue per added bidder remains strong even when there are already many bidders.
Markets for zero-day exploits (software vulnerabilities unknown to the vendor) have a long history and a growing popularity. We study these markets from a revenue-maximizing mechanism design perspective. We first propose a theoretical model for zero-day exploits markets. In our model, one exploit is being sold to multiple buyers. There are two kinds of buyers, which we call the defenders and the offenders. The defenders are buyers who buy vulnerabilities in order to fix them (e.g., software vendors). The offenders, on the other hand, are buyers who intend to utilize the exploits (e.g., nationa…
We study single-item single-unit Bayesian posted price auctions, where buyers arrive sequentially and their valuations for the item being sold depend on a random, unknown state of nature. The seller has complete knowledge of the actual state and can send signals to the buyers so as to disclose information about it. For instance, the state of nature may reflect the condition and/or some particular features of the item, which are known to the seller only. The problem faced by the seller is about how to partially disclose information about the state so as to maximize revenue. Unlike classical sig…
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…
Budgets play a significant role in real-world sequential auction markets such as those implemented by internet companies. To maximize the value provided to auction participants, spending is smoothed across auctions so budgets are used for the best opportunities. Motivated by a mechanism used in practice by several companies, this paper considers a smoothing procedure that relies on {\em pacing multipliers}: on behalf of each buyer, the auction market applies a factor between 0 and 1 that uniformly scales the bids across all auctions. Reinterpreting this process as a game between buyers, we int…
A standard result from auction theory is that bidding truthfully in a second price auction is a weakly dominant strategy. The result, however, does not apply in the presence of Cost Per Action (CPA) constraints. Such constraints exist, for instance, in digital advertising, as some buyer may try to maximize the total number of clicks while keeping the empirical Cost Per Click (CPC) below a threshold. More generally the CPA constraint implies that the buyer has a maximal average cost per unit of value in mind. We discuss how such constraints change some traditional results from auction theory. F…
We revisit the well-studied problem of budget-feasible procurement, where a buyer with a strict budget constraint seeks to acquire services from a group of strategic providers (the sellers). During the last decade, several strategyproof budget-feasible procurement auctions have been proposed, aiming to maximize the value of the buyer, while eliciting each seller's true cost for providing their service. These solutions predominantly take the form of randomized sealed-bid auctions: they ask the sellers to report their private costs and then use randomization to determine which subset of services…
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…
Periodic double auctions (PDA) have applications in many areas such as in e-commerce, intra-day equity markets, and day-ahead energy markets in smart-grids. While the trades accomplished using PDAs are worth trillions of dollars, finding a reliable bidding strategy in such auctions is still a challenge as it requires the consideration of future auctions. A participating buyer in a PDA has to design its bidding strategy by planning for current and future auctions. Many equilibrium-based bidding strategies proposed are complex to use in real-time. In the current exposition, we propose a scale-ba…
Federated Learning Incentive Mechanism under Buyers' Auction Market
University of Electronic Science and Technology of China（电子科技大学）；Beihang University（北京航空航天大学）；National Taiwan University（台湾大学）；Jiangxi University of Finance and Economics（江西财经大学）
Nanjing University of Science and Technology（南京理工大学）；University of Electronic Science and Technology of China（电子科技大学）；ShanghaiTech University（上海科技大学）
This paper studies multi-unit auctions powered by intermediaries, where each intermediary owns a private set of unit-demand buyers and all intermediaries are networked with each other. Our goal is to incentivize the intermediaries to diffuse the auction information to individuals they can reach, including their private buyers and neighboring intermediaries, so that more potential buyers are able to participate in the auction. To this end, we build a diffusion-based auction framework which incorporates the strategic interaction of intermediaries. It is showed that the classic Vickrey-Clarke-Gro…
We obtain revenue guarantees for the simple pricing mechanism of a single posted price, in terms of a natural parameter of the distribution of buyers' valuations. Our revenue guarantee applies to the single item n buyers setting, with values drawn from an arbitrary joint distribution. Specifically, we show that a single price drawn from the distribution of the maximum valuation Vmax = max {V_1, V_2, ...,V_n} achieves a revenue of at least a 1/e fraction of the geometric expecation of Vmax. This generic bound is a measure of how revenue improves/degrades as a function of the concentration/sprea…
In two-sided markets, Myerson and Satterthwaite's impossibility theorem states that one can not maximize the gain-from-trade while also satisfying truthfulness, individual-rationality and no deficit. Attempts have been made to circumvent Myerson and Satterthwaite's result by attaining approximately-maximum gain-from-trade: the double-sided auctions of McAfee (1992) is truthful and has no deficit, and the one by Segal-Halevi et al. (2016) additionally has no surplus --- it is strongly-budget-balanced. They consider two categories of agents --- buyers and sellers, where each trade set is compose…
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…
We consider the problem of an auctioneer who faces the task of selling a good (drawn from a known distribution) to a set of buyers, when the auctioneer does not have the capacity to describe to the buyers the exact identity of the good that he is selling. Instead, he must come up with a constrained signalling scheme: a (non injective) mapping from goods to signals, that satisfies the constraints of his setting. For example, the auctioneer may be able to communicate only a bounded length message for each good, or he might be legally constrained in how he can advertise the item being sold. Each …
