Diffusion auction design is a new trend in mechanism design for which the main goal is to incentivize existing buyers to invite new buyers, who are their neighbors on a social network, to join an auction even though they are competitors. With more buyers, a diffusion auction will be able to give a more efficient allocation and receive higher revenue. Existing studies have proposed many interesting diffusion auctions to attract more buyers, but the seller's revenue is not optimized. Hence, in this study, we investigate what optimal revenue the seller can achieve by attracting more buyers. Different from the traditional setting, the revenue that can be achieved in a diffusion auction highly relies on the structure of the network. Hence, we focus on optimal auctions with given classes of underlying networks. We propose a class of mechanisms, where for any given structure, an optimal diffusion mechanism can be found. We point out that it implies an idea of "reserve structure". Moreover, we show that an optimal mechanism that handles all structures does not exist. Therefore, we also propose mechanisms that have bounded approximations of the optimal revenue in all structures.
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…
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…
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 defau…
Diffusion auction is a new model in auction design. It can incentivize the buyers who have already joined in the auction to further diffuse the sale information to others via social relations, whereby both the seller's revenue and the social welfare can be improved. Diffusion auctions are essentially non-typical multidimensional mechanism design problems and agents' social relations are complicatedly involved with their bids. In such auctions, incentive-compatibility (IC) means it is best for every agent to honestly report her valuation and fully diffuse the sale information to all her neighbo…
In mechanism design, it is challenging to design the optimal auction with correlated values in general settings. Although value distribution can be further exploited to improve revenue, the complex correlation structure makes it hard to acquire in practice. Data-driven auction mechanisms, powered by machine learning, enable to design auctions directly from historical auction data, without relying on specific value distributions. In this work, we design a learning-based auction, which can encode the correlation of values into the rank score of each bidder, and further adjust the ranking rule to…
Bulow and Klemperer's well-known result states that, in a single-item auction where the $n$ bidders' values are independently and identically drawn from a regular distribution, the Vickrey auction with one additional bidder (a duplicate) extracts at least as much revenue as the optimal auction without the duplicate. Hartline and Roughgarden, in their influential 2009 paper, removed the requirement that the distributions be identical, at the cost of allowing the Vickrey auction to recruit $n$ duplicates, one from each distribution, and relaxing its revenue advantage to a $2$-approximation. In t…
Probabilistic Mechanism Design in Diffusion Auctions
School of Computer Science, Peking University（北京大学计算机学院）；Ant Group（蚂蚁集团）；National Engineering Research Center for Software Engineering, Peking University（北京大学软件工程国家工程研究中心）
What fraction of the single item $n$ buyers setting's expected optimal revenue MyeRev can the second price auction with reserves achieve? In the special case where the buyers' valuation distributions are all drawn i.i.d. and the distributions satisfy the regularity condition, the second price auction with an anonymous reserve (ASP) is the optimal auction itself. As the setting gets more complex, there are established upper bounds on the fraction of MyeRev that ASP can achieve. On the contrary, no such upper bounds are known for the fraction of MyeRev achievable by the second price auction with…
University of Electronic Science and Technology of China（电子科技大学）
In recent years, a new branch of auction models called diffusion auction has extended the traditional auction into social network scenarios. The diffusion auction models the auction as a networked market whose nodes are potential customers and whose edges are the relations between these customers. The diffusion auction mechanism can incentivize buyers to not only submit a truthful bid, but also further invite their surrounding neighbors to participate into the auction. It can convene more participants than traditional auction mechanisms, which leads to better optimizations of different key asp…
University of Electronic Science and Technology of China（中国电子科技大学）；ShanghaiTech University（上海科技大学）；Kyushu University（九州大学）
Auction is the common paradigm for resource allocation which is a fundamental problem in human society. Existing research indicates that the two primary objectives, the seller's revenue and the allocation efficiency, are generally conflicting in auction design. For the first time, we expand the domain of the classic auction to a social graph and formally identify a new class of auction mechanisms on graphs. All mechanisms in this class are incentive-compatible and also promote all buyers to diffuse the auction information to others, whereby both the seller's revenue and the allocation efficien…
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…
This paper develops tools for welfare and revenue analyses of Bayes-Nash equilibria in asymmetric auctions with single-dimensional agents. We employ these tools to derive price of anarchy results for social welfare and revenue. Our approach separates the standard smoothness framework into two distinct parts, isolating the analysis common to any auction from the analysis specific to a given auction. The first part relates a bidder's contribution to welfare in equilibrium to their contribution to welfare in the optimal auction using the price the bidder faces for additional allocation. Intuitive…
We study the communication complexity of incentive compatible auction-protocols between a monopolist seller and a single buyer with a combinatorial valuation function over $n$ items. Motivated by the fact that revenue-optimal auctions are randomized [Tha04,MV10,BCKW10,Pav11,HR15] (as well as by an open problem of Babaioff, Gonczarowski, and Nisan [BGN17]),we focus on the randomized communication complexity of this problem (in contrast to most prior work on deterministic communication). We design simple, incentive compatible, and revenue-optimal auction-protocols whose expected communication co…
我们认为优先级自由拍卖收入和福利最大化时，代理人有一个共同的预算。我们考虑的抽象环境是有一个向下封闭的和对称的可行性约束的代理服务的概率。这些环境包括位置拍卖，其中具有降低的点击率的位置被拍卖给广告商。我们将Hartline和Yan（2011）的无嫉妒基准推广和表征到有预算的环境中，并表征福利和收入的最佳无嫉妒结果。我们给出了近似这些基准的无先验机制。在我们的机制的一个组成部分是一个成交拍卖的位置拍卖环境。该拍卖是Dobzinski et al.（2008）的多单位成交拍卖的推广，也是Goel et al.（2012）的多面体成交拍卖的特例。对于福利最大化，我们表明，这种成交拍卖是一个很好的近似的嫉妒无最优福利的位置拍卖环境。对于利润最大化，我们推广了Fiat等人（2002）的随机抽样利润提取拍卖，用于数字商品，以给出对称下闭环境中无嫉妒最优收入的10.0近似值。即使没有预算，利润最大化问题也很有趣，我们的机制是一个7.5近似，改进了Ha和Hartline（2012）的30.4界限。
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…
The revenue optimal mechanism for selling a single item to agents with independent but non-identically distributed values is complex for agents with linear utility (Myerson,1981) and has no closed-form characterization for agents with non-linear utility (cf. Alaei et al., 2012). Nonetheless, for linear utility agents satisfying a natural regularity property, Alaei et al. (2018) showed that simply posting an anonymous price is an e-approximation. We give a parameterization of the regularity property that extends to agents with non-linear utility and show that the approximation bound of anonymou…
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…
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…
Consider Myerson's optimal auction with respect to an inaccurate prior, e.g., estimated from data, which is an underestimation of the true value distribution. Can the auctioneer expect getting at least the optimal revenue w.r.t. the inaccurate prior since the true value distribution is larger? This so-called strong revenue monotonicity is known to be true for single-parameter auctions when the feasible allocations form a matroid. We find that strong revenue monotonicity fails to generalize beyond the matroid setting, and further show that auctions in the matroid setting are the only downward-c…
Optimal transportation theory is an area of mathematics with real-world applications in fields ranging from economics to optimal control to machine learning. We propose a new algorithm for solving discrete transport (network flow) problems, based on classical auction methods. Auction methods were originally developed as an alternative to the Hungarian method for the assignment problem, so the classic auction-based algorithms solve integer-valued optimal transport by converting such problems into assignment problems. The general transport auction method we propose works directly on real-valued …
A diffusion auction is a market to sell commodities over a social network, where the challenge is to incentivize existing buyers to invite their neighbors in the network to join the market. Existing mechanisms have been designed to solve the challenge in various settings, aiming at desirable properties such as non-deficiency, incentive compatibility and social welfare maximization. Since the mechanisms are employed in dynamic networks with ever-changing structures, buyers could easily generate fake nodes in the network to manipulate the mechanisms for their own benefits, which is commonly know…
We explore the properties of optimal multi-dimensional auctions in a model where a single object of multiple qualities is sold to several buyers. Using simulations, we test some hypotheses conjectured by Belloni et al. [3] and Kushnir and Shourideh [7]. As part of this work, we provide the first open-source library for multi-dimensional auction simulations written in Python.
We study the problem of computing optimal prices for a version of the Product-Mix auction with budget constraints. In contrast to the ``standard'' Product-Mix auction, the objective is to maximize revenue instead of social welfare. We prove correctness of an algorithm proposed by Paul Klemperer and DotEcon which is sufficiently efficient in smaller markets.
