Second-price Auction Research Articles

Fast Core Pricing for Rich Advertising Auctions

Standard ad auction formats do not immediately extend to settings where multiple size configurations and layouts are available to advertisers. In these settings, the sale of web advertising space increasingly resembles a combinatorial auction with complementarities, where truthful auctions such as the Vickrey-Clarke-Groves (VCG) can yield unacceptably low revenue. We therefore study core selecting auctions, which boost revenue by setting payments so that no group of agents, including the auctioneer, can jointly improve their utilities by switching to a different outcome. Our main result is a combinatorial algorithm that finds an approximate bidder optimal core point with almost linear number of calls to the welfare maximization oracle. Our algorithm is faster than previously-proposed heuristics in the literature and has theoretical guarantees. We conclude that core pricing is implementable even for very time sensitive practical use cases such as realtime auctions for online advertising and can yield more revenue. We justify this claim experimentally using the Microsoft Bing Ad Auction data, through which we show our core pricing algorithm generates almost 26% more revenue than VCG on average, about 9% more revenue than other core pricing rules known in the literature, and almost matches the revenue of the standard Generalized Second Price (GSP) auction.

Decentralized Transactive Energy for Flexible Resources in Distribution Systems

The increasing penetration of proactive agents in electric power distribution systems calls for mechanisms to coordinate their trading activities. The commonly employed centralized and distributed methods for supply-demand coordination are not only limited by hardware requirements but also restrictive for active participation of the market agents. This paper proposes a novel decentralized transactive coordination framework that allows participants to bid and clear transactions via a bilateral interaction process. The framework is based on 1) power consumption flexibility individually reported by demand agents using model-predictive control, 2) bilateral supply-side bidding individually determined by the supply agents using a Markowitz Portfolio Optimization model, and 3) individual simultaneous clearing of transactions by demand agents based on second-price sealed-bid auctions. The suppliers bid in the market to achieve desired returns while minimizing their risks. The demand agents harness their demand flexibility by competitively clearing the supplier bids. Unlike traditional approaches, the proposed framework does not require master nodes to orchestrate transactions and, therefore, facilitates massive participation of market agents. Simulation cases demonstrate that the proposed framework successfully performs the market function for bilateral transactions among thousands of proactive agents.

Marketing Agencies and Collusive Bidding in Online Ad Auctions

The transition of the advertising market from traditional media to the internet has induced a proliferation of marketing agencies specialized in bidding in the auctions that are used to sell ad space on the web. We analyze how collusive bidding can emerge from bid delegation to a common marketing agency and how this can undermine the revenues and allocative efficiency of both the generalized second-price auction (GSP, used by Google, Microsoft Bing, and Yahoo!) and the Vickrey–Clarke–Groves (VCG) mechanism (used by Facebook). We find that despite its well-known susceptibility to collusion, the VCG mechanism outperforms the GSP auction in terms of both revenues and efficiency. This paper was accepted by Gabriel Weintraub, revenue management and market analytics.

Best-response dynamics in combinatorial auctions with item bidding

In a combinatorial auction with item bidding, agents participate in multiple single-item second-price auctions at once. As some items might be substitutes, agents need to strategize in order to maximize their utilities. A number of results indicate that high social welfare can be achieved this way, giving bounds on the welfare at equilibrium. Recently, however, criticism has been raised that equilibria of this game are hard to compute and therefore unlikely to be attained.In this paper, we take a different perspective by studying simple best-response dynamics. Often these dynamics may take exponentially long before they converge or they may not converge at all. However, as we show, convergence is not even necessary for good welfare guarantees. Given that agents' bid updates are aggressive enough but not too aggressive, the game will reach and remain in states of high welfare after each agent has updated his bid at least once.

Oracle-efficient Online Learning and Auction Design

We consider the design of computationally efficient online learning algorithms in an adversarial setting in which the learner has access to an offline optimization oracle. We present an algorithm called Generalized Follow-the-Perturbed-Leader and provide conditions under which it is oracle-efficient while achieving vanishing regret. Our results make significant progress on an open problem raised by Hazan and Koren [31], who showed that oracle-efficient algorithms do not exist in general [30] and asked whether one can identify properties under which oracle-efficient online learning may be possible. Our auction-design framework considers an auctioneer learning an optimal auction for a sequence of adversarially selected valuations with the goal of achieving revenue that is almost as good as the optimal auction in hindsight, among a class of auctions. We give oracle-efficient learning results for: (1) VCG auctions with bidder-specific reserves in single-parameter settings, (2) envy-free item pricing in multi-item auctions, and (3) s-level auctions of Morgenstern and Roughgarden [43] for single-item settings. The last result leads to an approximation of the overall optimal Myerson auction when bidders’ valuations are drawn according to a fast-mixing Markov process, extending prior work that only gave such guarantees for the i.i.d. setting. Finally, we derive various extensions, including: (1) oracle-efficient algorithms for the contextual learning setting in which the learner has access to side information (such as bidder demographics), (2) learning with approximate oracles such as those based on Maximal-in-Range algorithms, and (3) no-regret bidding in simultaneous auctions, resolving an open problem of Daskalakis and Syrgkanis [14].

Auction Design for Edge Computation Offloading in SDN-Based Ultra Dense Networks

Relying on offloading computation tasks to the network edge, ultra dense networks (UDNs) are capable of providing delay-aware service to nearby users. Meanwhile, software defined networking (SDN) is deemed as an effective technology to ease the management of infrastructure plane and control plane in UDNs, which is termed as SDN-based ultra dense networks. Specifically, the centralized SDN controller is capable of managing the whole network globally. With the increasing demands for various applications as well as the limitation of computation, storage and communication resource, how to allocate spectrum resource appropriately is imperative. In this article, we mainly show solicitude for spectrum sharing and edge computation offloading problems in SDN-based ultra dense networks, constituted of various macro base stations (MBSs), small-cell base stations (SBSs) and user equipments (UEs). To address this issue, we propose a second-price auction scheme for ensuring the fair bidding for spectrum rent, which enables the MBS edge cloud and SBS edge cloud to occupy the channel in cooperative and competitive modes. Moreover, the MBS edge cloud is termed as the buyer, and the SBS edge clouds are the sellers who sell the offloading resource to the MBS edge cloud. To be specific, the spectrum sharing and computation offloading scheme is executed in the SDN controller, and the controller is responsible for distributing spectrum allocation instructions to the infrastructure plane. Finally, experimental results validate the effectiveness of our proposed scheme in SDN-based ultra dense networks.

Peaches, lemons, and cookies: Designing auction markets with dispersed information

We study how ex ante information asymmetries affect revenue in common-value second-price auctions, motivated by online advertising auctions where “cookies” inform individual advertisers about advertising opportunities. We distinguish information structures in which cookies identify “lemons” (low-value impressions) from those in which cookies identify “peaches” (high-value impressions). As this setting features multiple Nash equilibria, we introduce a new refinement, “tremble robust equilibrium” (TRE) and characterize the unique TRE in first-price and second-price common-value auctions with two bidders who each receive a binary signal. We find that common-value second-price auction revenues are vulnerable to ex ante information asymmetry if relatively rare cookies identify lemons, but not if they identify peaches. First-price auction revenues are substantially higher than second-price auction revenues under these conditions. Extensions show that these insights are robust.

Revenue-Optimal Auction For Resource Allocation in Wireless Virtualization: A Deep Learning Approach

Wireless virtualization has become a key concept in future cellular networks which can provide multiple virtualized wireless networks for different mobile virtual network operators (MVNOs) over the same physical infrastructure. Resource allocation is a main challenging issue in wireless virtualization for which auction approaches have been widely used. However, for most existing auction-based allocation schemes, the objective is to maximize the social welfare (i.e., the sum of all valuations of winning bidders) due to its simplicity. While in reality, MVNOs are more interested in maximizing their own revenues (i.e., received payments from auction winners). However, the revenue-optimal auction problem is much more complex since the payment price is unknown before calculation. In this paper, we aim to design a revenue-optimal auction mechanism for resource allocation in wireless virtualization. Considering the complexity, deep learning techniques are applied. Specifically, we construct a multi-layer feed-forward neural network based on the analysis of optimal auction design. The neural network adopts users’ bids as the input and the allocation rule and conditional payment rule for the users as the output. The proposed auction mechanism possesses several desirable properties, e.g., individual rationality, incentive compatibility and budget constraint. Finally, simulation results demonstrate the effectiveness of the proposed scheme. Comparing with second-price auction and optimization-based schemes, the proposed scheme can increase the revenue by 10 and 30 percent on average, for single MVNO and multi-MVNO cases, respectively.

A Blockchain-Enabled Multi-Settlement Quasi-Ideal Peer-to-Peer Trading Framework

The concept of peer-to-peer (P2P) trading, or transactive energy (TE), is gaining momentum as a future grid restructure. It has the potentials to utilize distributed energy resources (DERs), proactive demand side management (DSM), and the infusion in information and communication technologies (e.g., blockchain and Internet of Things (IoT)) for promoting the technical and economic efficiency of the system in its entirety. An efficient market framework is vital for the successful and sustainable implementation of such a concept. This article proposes a P2P energy trading framework enabled by blockchain. It consolidates bilateral contracts, an electronic-commerce platform, a double-auction Vickrey-Clarke-Groves (VCG) mechanism, and trading functionalities with the main grid. Through these multi-layer mechanisms, various trading preferences and attributes of electricity generation and/or consumption are accommodated. Meanwhile, the VCG mechanism eliminates any potential for market power exercise via incentivizing truthful bidding of participants. Different remedies are proposed to overcome the drawback of VCG, i.e., the lack of balanced-budget property. Accordingly, the proposed trading framework is described as multi-settlement and quasi-ideal. Case studies are conducted to analyze and evaluate the proposed trading framework and demonstrate the effectiveness of the proposed remedies in handling probable market deficiencies.

Downstream mergers in vertically related markets with capacity constraints

Motivated by a recent merger proposal in the French outdoor advertising market, we develop a model in which firms are initially endowed with some advertising capacities and compete on two fronts. First, firms compete to acquire additional advertising capacities on an upstream market; a first stage modeled as a second-price auction with externalities. Second, those firms, privately informed on their own costs, use their capacities on the downstream market to supply advertisers whose demand is random; a second stage modeled by means of mechanism design techniques. We study the linkages between the equilibrium outcomes on both markets. When a firm is endowed with more initial capacity, through the acquisition of a competitor for instance, whether it becomes more or less eager to acquire extra capacity on the upstream market depends a priori on fine details of the downstream market. Under reasonable choices of functional forms, we demonstrate that a downstream merger does not create any bias in the upstream market towards the already dominant firm.

Are non-farming consumers willing to pay “a good market price” for iron-biofortified finger millet? Evidence from experimental auctions in Karnataka, India

PurposeBiofortification of staple crops is a promising strategy to alleviate micronutrient deficiencies in rural populations of the developing world. The possibility to sell biofortified crops at “a good market price” plays a vital role for the acceptance by smallholder farmers. This study is therefore focused on non-farming consumers' willingness to pay (WTP) for biofortified crops.Design/methodology/approachSpecifically, we elicited non-farming consumers' WTP a premium for the improved iron content (+30% iron) in a 1kg finger millet bag using a 2nd price Vickrey auction with six auction rounds and one health- and one process-related information treatment. Due to multiple bids per subject, premiums were analyzed using a linear mixed-effects model, controlling for market feedback and auction round.FindingsDespite more than half of the respondents being skeptical toward new crop varieties, the acceptance rate was very high (98% with a WTP above zero). The average premium amounted to 27% and could be significantly increased with the provision of health-related information. In contrast, information about the breeding method was ineffective. The WTP was significantly higher for higher income and lower for higher age, education and skepticism toward new crop varieties and increased with increasing rounds.Research limitations/implicationsOur results suggest that non-farming consumers are willing to pay “a good market price” for iron-biofortified finger millet. Our analysis also confirms the importance of health-related information for raising consumers' WTP. This information supports the further development and introduction of biofortified crops to alleviate micronutrient malnutrition.Originality/valueThis study adds to the still limited literature on consumers' WTP for iron-biofortified crops in India, focusing on non-farming consumers to assess the price such crops can achieve on the market.

Robust Auctions for Revenue via Enhanced Competition

In “Robust Auctions for Revenue via Enhanced Competition,” T. Roughgarden, I. Talgam-Cohen, and Q. Yan revisit the classic Bulow–Klemperer result. This result compares the revenues of two well-known auction formats: the welfare-maximizing Vickrey auction and the revenue-maximizing Myerson auction. It shows that, with an extra bidder competing for the item, the Vickrey auction becomes as good as the Myerson auction in terms of revenue while maintaining independence from prior distributional information about bidders’ valuations. Unfortunately, Myerson’s toolbox for revenue-optimal auction design does not extend to combinatorial auctions with multiple heterogenous items, for which optimizing revenue remains a challenge—especially if we want auction designs that are simple and robust enough to use in practice. This paper extends the Bulow–Klemperer result to multiple heterogenous items by showing that a prior-independent, simple, welfare-maximizing auction with additional competing bidders achieves as much revenue as the ill-understood optimal auction.

Auction based game theory in cognitive radio networks for dynamic spectrum allocation

Cognitive radio is an emerging technology that has a high potential to deal with the scarcity problem in the radio spectrum. Dynamic spectrum access in cognitive networks enhances the efficiency of spectral utilization by cognitive users (unlicensed users). Auction mechanism approach helps the cognitive users to get a part of the unused license band, for a lease, from the primary users (licensed users). Based on the interference constraints, auction methods share the leased band to many cognitive users with negligible mutual interference. Because of this unique feature, the multi-winner auction is a fresh challenge to the existing auction mechanisms like (Vickrey–Clarke-Groves) VCG and Second price auction. The proposed method uses interference-based constraints and satisfaction levels among the cognitive users to select the winner of the pricing based game. In this paper, a new framework plans to manipulate the multi-winner auction mechanism, based upon a pricing strategy to overcome the drawbacks of the traditional mechanisms. The proposed mechanism enhances the spectral efficiency of the cognitive users and also motivates the primary users to lease the bands to the cognitive users, with increased primary user revenue. Fairness among cognitive users ensures this mechanism. Simulation results show that our mechanism increases the spectral efficiency of cognitive users and the revenue of primary users.

Optimal monotone signals in Bayesian persuasion mechanisms

This paper develops a new approach—based on the majorization theory—to the information design problem in Bayesian persuasion mechanisms, i.e., models in which the sender selects the signal structure of the agent(s) who then reports it to the non-strategic receiver. We consider a class of mechanisms in which the posterior payoff of the sender depends on the value of a realized posterior mean of the state, its order in the sequence of possible means, and the marginal distribution of signals. We provide a simple characterization of mechanisms in which optimal signal structures are monotone partitional. Our approach has two economic implications: it is invariant to monotone transformations of the state and allows to decompose setups with multiple agents into independent Bayesian persuasion mechanisms with a single agent. As the main application of our characterization, we show the optimality of monotone partitional signal structures in all selling mechanisms with independent private values and quasi-linear preferences. We also provide sharp characterization of optimal signal structures for second-price auctions and posted-price sales.

Mechanism design for on-demand first-mile ridesharing

Ridesharing emerges as a viable way to bridge the first-mile accessibility gap to public transit. There is particularly a high demand for the first-mile ridesharing service in transit-intensive metropolitan areas. This paper studies the mechanism design problem in order to promote passengers’ participation in the on-demand first-mile ridesharing accounting for passengers’ mobility preferences, including passengers’ requirements on arrival deadlines, maximum willing-to-pay prices, and detour tolerances. A rolling horizon planning approach is used to process spontaneous on-demand passenger requests. We propose a novel mechanism, namely “Mobility-Preference-Based Mechanism with Baseline Price Control” (MPMBPC), which adapts the traditional Vickrey–Clarke–Groves (VCG) mechanism and incorporates a baseline price control component. MPMBPC is proved to satisfy several important mechanism design properties, including “individual rationality”, “incentive compatibility”, “price controllability”, and “detour discounting reasonability”. In comparison with the traditional general-purpose VCG mechanism, MPMBPC can avoid unreasonably low prices and prevent carriers’ deficits. A computationally efficient heuristic algorithm called Solution Pooling Approach (SPA) is developed to solve large-scale ridesharing mechanism design problems. Numerical examples are developed to demonstrate that SPA can solve large-scale ridesharing mechanism design problems in a computationally efficient way, with satisfactory solution qualities.

Willingness-to-Pay for Eco-Labelled Forest Products in Northern Ireland: An Experimental Auction Approach

Woodlands provide a variety of market and non-market benefits, but deforestation arising from pressures on landowners to clear forested areas for other land uses may cause irrevocable loss of these benefits. Landowners need to be encouraged to create or retain wooded areas on their land, and manage them sustainably.A proposed solution is the use of an eco-labelling scheme. Eco-labelling is a process by which branding is applied to a product to assure a customer that the product is “environmentally-friendly”. Customers are willing to pay more for eco-labelled forest products and eco-labels allow producers of forest products to differentiate themselves in the market or enter new markets entirely. It acts as a market-based instrument to encourage sustainable forest management.Through the use of an experimental second price Vickrey auction, this study determined that people are willing to pay an average of 88p more for every £1 on a low cost, frequently purchased eco-labelled wood product. This positive willingness-to-pay is related to the consumers’ knowledge of the environment, their conservation-orientated beliefs and higher levels of education. Information presented also determines willingness-to-pay, with consumers favouring less information about the product's credentials, preferring to be told the product is generally “eco-friendly” and “sustainable”.

Data‐driven virtual power plant bidding package model and its application to virtual VCG auction‐based real‐time power market

Energy storage and virtual power plant technologies have been developed and become important technical means to enhance power system stability and reduce real-time dispatching costs. In this study, the dispatching capability and dispatching cost characteristics of the virtual power plants are analysed firstly in detail, as well as the dispatching difficulties under the traditional market modes. Hence, virtual power plant real-time bidding package model and virtual auction-based real-time power market mechanism are proposed. Data-driven virtual power plant real-time packing method and bidding package model integrated virtual Vickrey–Clarke–Groves auction model are put forward. Finally, the feasibility and validity of the proposed mechanism and method are verified by case studies and result in analyses of the IEEE-30 bus test system with multiple virtual power plants, providing a scientific foundation and a practical solution to the real-time power market.

Truthful Auction Analysis and Design in Multiunit Heterogenous Spectrum Markets With Reserve Prices

We a practical multiunit heterogeneous spectrum market in which each buyer may request multiple channels with different bid prices at different geographical regions and each channel is associated with a reserve price indicating the desired revenue of the seller. The degree-of-freedom brought by multiunit trading and (reserve and bid) price diversity in such a market can be exploited to break the truthfulness of the two most popular schemes adopted by secondary spectrum auctions, namely Myerson’s Optimal Mechanism (MOM) and Vickrey-Clarke-Groves (VCG), via bidder self-collusion. In this paper, we conduct a thorough analysis on the root causes of untruthfulness in MOM and VCG, and prove the fundamental theories addressing when MOM and VCG are truthful and when their truthfulness is broken by bid rigging. Particularly, we demonstrate how self-collusion is exploited in MOM and VCG to improve the untruthful bidders’ utility. The critical findings provide a guidance for us to design a Self-collusion Resistant Auction (SIRI) in multiunit heterogeneous spectrum markets with reserve prices. The economic properties of SIRI are proved via rigorous theoretical analysis.

Coordination of Purchasing and Bidding Activities Across Markets

In both consumer purchasing and industrial procurement, combinatorial interdependencies among the items to be purchased are commonplace. E-commerce compounds the problem by providing more opportunities for switching suppliers at low costs, but also potentially eases the problem by enabling automated market decision-making systems, commonly referred to as trading agents, to make purchasing decisions in an integrated manner across markets. Most of the existing research related to trading agents assumes that there exists a combinatorial market mechanism in which buyers (or sellers) can bid (or sell) service or merchant bundles. Today's prevailing e-commerce practice, however, does not support this assumption in general and thus limits the practical applicability of these approaches. We are investigating a new approach to deal with the combinatorial interdependency challenges for online markets. This approach relies on existing commercial online market institutions such as posted-price markets and various online auctions that sell single items. It uses trading agents to coordinate a buyer's purchasing and bidding activities across multiple online markets simultaneously to achieve the best overall procurement effectiveness. This paper presents two sets of models related to this approach. The first set of models formalizes optimal purchasing decisions across posted-price markets with fixed transaction costs. Flat shipping costs, a common e-tailing practice, are captured in these models. We observe that making optimal purchasing decisions in this context is NP-hard in the strong sense and suggest several efficient computational methods based on discrete location theory. The second set of models is concerned with the coordination of bidding activities across multiple online auctions. We study the underlying coordination problem for a collection of first or second-price sealed-bid auctions and derive the optimal coordination and bidding policies.

Unimodal Bandits with Continuous Arms

We consider stochastic bandit problems with a continuous set of arms and where the expected reward is a continuous and unimodal function of the arm. For these problems, we propose the Stochastic Polychotomy (SP) algorithms, and derive finite-time upper bounds on its regret and optimization error. We show that, for a class of reward functions, the SP algorithm achieves a regret and an optimization error with optimal scalings, i.e., $O(\sqrtT )$ and $O(1/\sqrtT )$ (up to a logarithmic factor), respectively. SP constitutes the first order-optimal algorithm for non-smooth expected reward functions, as well as for smooth functions with unknown smoothness. The algorithm is based on sequential statistical tests used to successively trim an interval that contains the best arm with high probability. These tests exhibit a minimal sample complexity which confers to SP its adaptivity and optimality. Numerical experiments actually reveal that the algorithm even outperforms state-of-the-art algorithms that exploit the knowledge of the smoothness of the reward function. The performance of SP is further illustrated on the problem of setting optimal reserve prices in repeated second-price auctions; there, the algorithm is evaluated on real-world data.