研究委托竞拍下的资源分配问题，通过 Price of Anarchy 分析表明，传统最高价拍卖效率低，而结合特定预算规则的 Trading Post 机制能对所有广义 p-均值目标实现较小效率损失。
摘要：
我们考虑一个设计者的问题，该设计者希望将资源分配给代表，然后由代表将他们收到的资源在他们所代表的个体之间进行分配。受美国最大的慈善机构之一 Feeding America 将捐赠分配给食物银行，然后食物银行再将捐赠进一步分配给食物无保障个体的方式的启发，我们专注于使用人造货币的机制。我们通过 Price of Anarchy 的视角比较了拍卖，涉及三个经典的福利目标：功利主义社会福利（个体效用之和）、Nash 社会福利（个体效用之积）和平均主义社会福利（个体效用之最小值）。我们证明了在温和的技术约束下，所有将每个物品分配给最高出价者的拍卖的 Price of Anarchy 的强下界；这包括 Feeding America 当前的拍卖，即 First-Price 拍卖。形成鲜明对比的是，我们的主要结果表明，将 Shapley 和 Shubik 的经典 Trading Post 机制适应于此设置，并结合 Feeding America 的预算规则选择（每个代表获得的人造货币数量等于其代表的个体数量），能同时对所有广义 $p$-均值目标实现较小的 Price of Anarchy。我们对 Trading Post 机制的 Price of Anarchy 的界限取决于 $\ell$：底层估值矩阵的秩和“不相干性”的乘积，它们共同捕捉了矩阵的值“分散程度”的概念。这个概念在矩阵补全文献中极具影响力，据我们所知，在我们之前从未在拍卖理论中使用过。也许令人惊讶的是，我们证明了对 $\ell$ 的依赖是必要的：Trading Post 机制的 Price of Anarchy 是 $\Omega(\sqrt{\ell})$。
英文摘要：
We consider the problem of a designer who wants to allocate resources to representatives, that then distribute the resources they receive among the individuals they represent. Motivated by the way Feeding America, one of the largest U.S. charities, allocates donations to food banks, which then further distribute the donations to food-insecure individuals, we focus on mechanisms that use artificial currencies. We compare auctions through the lens of the Price of Anarchy, with respect to three canonical welfare objectives: utilitarian social welfare (sum of individuals' utilities), Nash social welfare (product of individuals' utilities), and egalitarian social welfare (minimum of individuals' utilities). We prove strong lower bounds on the Price of Anarchy of all auctions that allocate each item to the highest bidder, subject to a mild technical constraint; this includes Feeding America's current auction, the First-Price auction. In sharp contrast, our main result shows that adapting the classic Trading Post mechanism of Shapley and Shubik to this setting, and coupled with Feeding America's choice of budget rule (each representative gets an amount of artificial currency equal to the number of individuals it represents), achieves a small Price of Anarchy for all generalized $p$-mean objectives simultaneously. Our bound on the Price of Anarchy of the Trading Post mechanism depends on $\ell$: the product of the rank and the ``incoherence'' of the underlying valuation matrix, which together capture a notion of how ``spread out'' the values of a matrix are. This notion has been extremely influential in the matrix completion literature, and, to the best of our knowledge, has never been used in auction theory prior to our work. Perhaps surprisingly, we prove that the dependence on $\ell$ is necessary: the Price of Anarchy of the Trading Post mechanism is $Ω(\sqrt{\ell})$.
Delegation covers a broad class of problems in which a principal doesn't have the resources or expertise necessary to complete a task by themselves, so they delegate the task to an agent whose interests may not be aligned with their own. Stochastic probing describes problems in which we are tasked with maximizing expected utility by "probing" known distributions for acceptable solutions subject to certain constraints. In this work, we combine the concepts of delegation and stochastic probing into a single mechanism design framework which we term delegated stochastic probing. We study how much …
Auto-bidding plays an important role in online advertising and has become a crucial tool for advertisers and advertising platforms to meet their performance objectives and optimize the efficiency of ad delivery. Advertisers employing auto-bidding only need to express high-level goals and constraints, and leave the bid optimization problem to the advertising platforms. As auto-bidding has obviously changed the bidding language and the way advertisers participate in the ad auction, fundamental investigation into mechanism design for auto-bidding environment should be made to study the interactio…
This paper gives a theoretical model for design and analysis of mechanisms for online marketplaces where a bidding dashboard enables the bid-optimization of long-lived agents. We assume that a good allocation algorithm exists when given the true values of the agents and we develop online winner-pays-bid and all-pay mechanisms that implement the same outcome of the algorithm with the aid of a bidding dashboard. The bidding dashboards that we develop work in conjunction with the mechanism to guarantee that bidding according to the dashboard is strategically equivalent (with vanishing utility dif…
From skipped exercise classes to last-minute cancellation of dentist appointments, underutilization of reserved resources abounds. Likely reasons include uncertainty about the future, further exacerbated by present bias. In this paper, we unite resource allocation and commitment devices through the design of contingent payment mechanisms, and propose the two-bid penalty-bidding mechanism. This extends an earlier mechanism proposed by Ma et al. (2019), assigning the resources based on willingness to accept a no-show penalty, while also allowing each participant to increase her own penalty in or…
In this work we consider selling items using a sequential first price auction mechanism. We generalize the assumption of conservative bidding to extensive form games (henceforth optimistic conservative bidding), and show that for both linear and unit demand valuations, the only pure subgame perfect equilibrium where buyers are bidding in an optimistic conservative manner is the minimal Walrasian equilibrium. In addition, we show examples where without the requirement of conservative bidding, subgame perfect equilibria can admit a variety of unlikely predictions, including high price of anarchy…
We perform a simulation-based analysis of keyword auctions modeled as one-shot games of incomplete information to study a series of mechanism design questions. Our first question addresses the degree to which incentive compatibility fails in generalized second-price (GSP) auctions. Our results suggest that sincere bidding in GSP auctions is a strikingly poor strategy and a poor predictor of equilibrium outcomes. We next show that the rank-by-revenue mechanism is welfare optimal, corroborating past results. Finally, we analyze profit as a function of auction mechanism under a series of alternat…
Interactions between bids to show ads online can lead to an advertiser's ad being shown to more men than women even when the advertiser does not target towards men. We design bidding strategies that advertisers can use to avoid such emergent discrimination without having to modify the auction mechanism. We mathematically analyze the strategies to determine the additional cost to the advertiser for avoiding discrimination, proving our strategies to be optimal in some settings. We use simulations to understand other settings.
We are interested in mechanisms that maximize social welfare. In [1] this problem was studied for multi-unit auctions with unit demand bidders and for the public project problem, and in each case social welfare undominated mechanisms in the class of feasible and incentive compatible mechanisms were identified. One way to improve upon these optimality results is by allowing the players to move sequentially. With this in mind, we study here sequential versions of two feasible Groves mechanisms used for single item auctions: the Vickrey auction and the Bailey-Cavallo mechanism. Because of the abs…
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 two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the winner or payoff of the game. We study {\em bidding games} in which the players bid for the right to move the token. Several bidding rules were studied previously. In {\em Richman} bidding, in each round, the players simultaneously submit bids, and the higher bidder moves the token and pays the other player. {\em Poorman} bidding is similar except that the winner of the bidding pays the "bank" rather than the other player. {\em Taxman} bidding spans the spectrum between Ric…
Cloud computing has been an emerging model which aims at allowing customers to utilize computing resources hosted by Cloud Service Providers (CSPs). More and more consumers rely on CSPs to supply computing and storage service on the one hand, and CSPs try to attract consumers on favorable terms on the other. In such competitive cloud computing markets, pricing policies are critical to market efficiency. While CSPs often publish their prices and charge users according to the amount of resources they consume, auction mechanism is rarely applied. In fact a feasible auction mechanism is the most e…
We address the problem of improving bidders' strategies in prior-dependent revenue-maximizing auctions and introduce a simple and generic method to design novel bidding strategies if the seller uses past bids to optimize her mechanism. We propose a simple and agnostic strategy, independent of the distribution of the competition, that is robust to mechanism changes and local (as opposed to global) optimization of e.g. reserve prices by the seller. This strategy guarantees an increase in utility compared to the truthful strategy for any distribution of the competition. In textbook-style examples…
In this paper, we deal with the uncertainty of bidding for display advertising. Similar to the financial market trading, real-time bidding (RTB) based display advertising employs an auction mechanism to automate the impression level media buying; and running a campaign is no different than an investment of acquiring new customers in return for obtaining additional converted sales. Thus, how to optimally bid on an ad impression to drive the profit and return-on-investment becomes essential. However, the large randomness of the user behaviors and the cost uncertainty caused by the auction compet…
We study a class of manipulations in combinatorial auctions where bidders fundamentally misrepresent what goods they are interested in. Prior work has largely assumed that bidders only submit bids on their bundles of interest, which we call simple bidding: strategizing over the bid amounts, but not the bundle identities. However, we show that there exists an entire class of auction instances for which simple bids are never optimal in Bayes-Nash equilibrium, always being strictly dominated by complex bids (where bidders bid on goods they are not interested in). We show this result for the two m…
As an emerging decentralized secure data management platform, blockchain has gained much popularity recently. To maintain a canonical state of blockchain data record, proof-of-work based consensus protocols provide the nodes, referred to as miners, in the network with incentives for confirming new block of transactions through a process of "block mining" by solving a cryptographic puzzle. Under the circumstance of limited local computing resources, e.g., mobile devices, it is natural for rational miners, i.e., consensus nodes, to offload computational tasks for proof of work to the cloud/fog c…
The increasing competition in digital advertising induced a proliferation of media agencies playing the role of intermediaries between advertisers and platforms selling ad slots. When a group of competing advertisers is managed by a common agency, many forms of collusion, such as bid rigging, can be implemented by coordinating bidding strategies, dramatically increasing advertisers' value. We study the problem of finding bids and monetary transfers maximizing the utility of a group of colluders, under GSP and VCG mechanisms. First, we introduce an abstract bid optimization problem -- called we…
We introduce a new numerical framework to learn optimal bidding strategies in repeated auctions when the seller uses past bids to optimize her mechanism. Crucially, we do not assume that the bidders know what optimization mechanism is used by the seller. We recover essentially all state-of-the-art analytical results for the single-item framework derived previously in the setup where the bidder knows the optimization mechanism used by the seller and extend our approach to multi-item settings, in which no optimal shading strategies were previously known. Our approach yields substantial increases…
The simultaneous multiple-round auction (SMRA) and the combinatorial clock auction (CCA) are the two primary mechanisms used to sell bandwidth. Under truthful bidding, the SMRA is known to output a Walrasian equilibrium that maximizes social welfare provided the bidder valuation functions satisfy the gross substitutes property. Recently, it was shown that the combinatorial clock auction (CCA) provides good welfare guarantees for general classes of valuation functions. This motivates the question of whether similar welfare guarantees hold for the SMRA in the case of general valuation functions.…
In classic auction theory, reserve prices are known to be effective for improving revenue for the auctioneer against quasi-linear utility maximizing bidders. The introduction of reserve prices, however, usually do not help improve total welfare of the auctioneer and the bidders. In this paper, we focus on value maximizing bidders with return on spend constraints -- a paradigm that has drawn considerable attention recently as more advertisers adopt auto-bidding algorithms in advertising platforms -- and show that the introduction of reserve prices has a novel impact on the market. Namely, by ch…
We establish a general optimization framework for the design of automated bidding agent in dynamic online marketplaces. It optimizes solely for the buyer's interest and is agnostic to the auction mechanism imposed by the seller. As a result, the framework allows, for instance, the joint optimization of a group of ads across multiple platforms each running its own auction format. Bidding strategy derived from this framework automatically guarantees the optimality of budget allocation across ad units and platforms. Common constraints such as budget delivery schedule, return on investments and gu…
SRI International（SRI国际）；University of British Columbia（不列颠哥伦比亚大学）
Market-based mechanisms such as auctions are being studied as an appropriate means for resource allocation in distributed and mulitagent decision problems. When agents value resources in combination rather than in isolation, they must often deliberate about appropriate bidding strategies for a sequence of auctions offering resources of interest. We briefly describe a discrete dynamic programming model for constructing appropriate bidding policies for resources exhibiting both complementarities and substitutability. We then introduce a continuous approximation of this model, assuming that money…
Many popular search engines run an auction to determine the placement of advertisements next to search results. Current auctions at Google and Yahoo! let advertisers specify a single amount as their bid in the auction. This bid is interpreted as the maximum amount the advertiser is willing to pay per click on its ad. When search queries arrive, the bids are used to rank the ads linearly on the search result page. The advertisers pay for each user who clicks on their ad, and the amount charged depends on the bids of all the advertisers participating in the auction. In order to be effective, adv…
There are many settings in which a principal performs a task by delegating it to an agent, who searches over possible solutions and proposes one to the principal. This describes many aspects of the workflow within organizations, as well as many of the activities undertaken by regulatory bodies, who often obtain relevant information from the parties being regulated through a process of delegation. A fundamental tension underlying delegation is the fact that the agent's interests will typically differ -- potentially significantly -- from the interests of the principal, and as a result the agent …
We consider the problem of the optimization of bidding strategies in prior-dependent revenue-maximizing auctions, when the seller fixes the reserve prices based on the bid distributions. Our study is done in the setting where one bidder is strategic. Using a variational approach, we study the complexity of the original objective and we introduce a relaxation of the objective functional in order to use gradient descent methods. Our approach is simple, general and can be applied to various value distributions and revenue-maximizing mechanisms. The new strategies we derive yield massive uplifts c…
Advertisers in online ad auctions are increasingly using auto-bidding mechanisms to bid into auctions instead of directly bidding their value manually. One prominent auto-bidding format is the target cost-per-acquisition (tCPA) which maximizes the volume of conversions subject to a return-of-investment constraint. From an auction theoretic perspective however, this trend seems to go against foundational results that postulate that for profit-maximizing bidders, it is optimal to use a classic bidding system like marginal CPA (mCPA) bidding rather than using strategies like tCPA. In this paper w…
Digital advertising constitutes one of the main revenue sources for online platforms. In recent years, some advertisers tend to adopt auto-bidding tools to facilitate advertising performance optimization, making the classical \emph{utility maximizer} model in auction theory not fit well. Some recent studies proposed a new model, called \emph{value maximizer}, for auto-bidding advertisers with return-on-investment (ROI) constraints. However, the model of either utility maximizer or value maximizer could only characterize partial advertisers in real-world advertising platforms. In a mixed enviro…
This paper focuses on the coordination of a population of thermostatically controlled loads (TCLs) with unknown parameters to achieve group objectives. The problem involves designing the device bidding and market clearing strategies to motivate self-interested users to realize efficient energy allocation subject to a peak energy constraint. This coordination problem is formulated as a mechanism design problem, and we propose a mechanism to implement the social choice function in dominant strategy equilibrium. The proposed mechanism consists of a novel bidding and clearing strategy that incorpo…
In this paper, we analyze a natural learning algorithm for uniform pacing of advertising budgets, equipped to adapt to varying ad sale platform conditions. On the demand side, advertisers face a fundamental technical challenge in automating bidding in a way that spreads their allotted budget across a given campaign subject to hidden, and potentially dynamic, cost functions. This automation and calculation must be done in runtime, implying a necessarily low computational cost for the high frequency auction rate. Advertisers are additionally expected to exhaust nearly all of their sub-interval (…
There are two major ways of selling impressions in display advertising. They are either sold in spot through auction mechanisms or in advance via guaranteed contracts. The former has achieved a significant automation via real-time bidding (RTB); however, the latter is still mainly done over the counter through direct sales. This paper proposes a mathematical model that allocates and prices the future impressions between real-time auctions and guaranteed contracts. Under conventional economic assumptions, our model shows that the two ways can be seamless combined programmatically and the publis…
We study the design of mechanisms in combinatorial auction domains. We focus on settings where the auction is repeated, motivated by auctions for licenses or advertising space. We consider models of agent behaviour in which they either apply common learning techniques to minimize the regret of their bidding strategies, or apply short-sighted best-response strategies. We ask: when can a black-box approximation algorithm for the base auction problem be converted into a mechanism that approximately preserves the original algorithm's approximation factor on average over many iterations? We present…
The Bidding Games: Reinforcement Learning for MEV Extraction on Polygon Blockchain
Independent Researcher（独立研究者）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Skolkovo Institute of Science and Technology（斯克尔科沃科学与技术研究所）；HSE University（俄罗斯伏尔加格勒国立高等经济大学）
Generalized Second Price (GSP) auctions are widely used by search engines today to sell their ad slots. Most search engines have supported broad match between queries and bid keywords when executing GSP auctions, however, it has been revealed that GSP auction with the standard broad-match mechanism they are currently using (denoted as SBM-GSP) has several theoretical drawbacks (e.g., its theoretical properties are known only for the single-slot case and full-information setting, and even in this simple setting, the corresponding worst-case social welfare can be rather bad). To address this iss…
Large Language Models as Bidding Agents in Repeated HetNet Auction
College of Science and Engineering（科学与工程学院）；Hamad Bin Khalifa University（哈马德·本·卡西姆大学）；CNRS（国家科学研究中心）；Universite de Lorraine（洛林大学）；CRAN（CRAN研究中心）；Department of Computer Science（计算机科学系）；Khalifa University（卡西姆大学）
Spot electricity markets are considered under a Game-Theoretic framework, where risk averse players submit orders to the market clearing mechanism to maximise their own utility. Consistent with the current practice in Europe, the market clearing mechanism is modelled as a Social Welfare Maximisation problem, with zonal pricing, and we consider inflexible demand, physical constraints of the electricity grid, and capacity-constrained producers. A novel type of non-parametric risk aversion based on a defined worst case scenario is introduced, and this reduces the dimensionality of the strategy va…
We study the inefficiency of mixed equilibria, expressed as the price of anarchy, of all-pay auctions in three different environments: combinatorial, multi-unit and single-item auctions. First, we consider item-bidding combinatorial auctions where m all-pay auctions run in parallel, one for each good. For fractionally subadditive valuations, we strengthen the upper bound from 2 [Syrgkanis and Tardos STOC'13] to 1.82 by proving some structural properties that characterize the mixed Nash equilibria of the game. Next, we design an all-pay mechanism with a randomized allocation rule for the multi-…
