Second-price Auction Research Articles

Auction-Promoted Trading for Multiple Federated Learning Services in UAV-Aided Networks

Federated learning (FL) represents a promising distributed machine learning paradigm that allows smart devices to collaboratively train a shared model via providing local data sets. However, problems considering multiple co-existing FL services and different types of service providers are rarely studied. In this paper, we investigate a multiple FL service trading problem in Unmanned Aerial Vehicle (UAV)-aided networks, where FL service demanders (FLSDs) aim to purchase various data sets from feasible clients (smart devices, e.g., smartphones, smart vehicles), and model aggregation services from UAVs, to fulfill their requirements. An auction-based trading market is established to facilitate the trading among three parties, i.e., FLSDs acting as buyers, distributed located client groups acting as data-sellers, and UAVs acting as UAV-sellers. The proposed auction is formalized as a 0-1 integer programming problem, aiming to maximize the overall buyers’ revenue via investigating winner determination and payment rule design. Specifically, since two seller types (data-sellers and UAV-sellers) are considered, an interesting idea integrating <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">seller pair</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">joint bid</i> is introduced, which turns diverse sellers into virtual seller pairs. Vickrey-Clarke-Groves (VCG)-based, and one-sided matching-based mechanisms are proposed, respectively, where the former achieves the optimal solutions, which, however, is computationally intractable. While the latter can obtain suboptimal solutions that approach to the optimal ones, with low computational complexity, especially upon considering a large number of participants. Significant properties such as truthfulness and individual rationality are comprehensively analyzed for both mechanisms. Extensive experimental results verify the properties and demonstrate that our proposed mechanisms outperform representative methods significantly.

Distributionally robust pricing in independent private value auctions

A seller chooses a reserve price in a second-price auction to maximize worst-case expected revenue when she knows only the mean of value distribution and an upper bound on either values themselves or variance. Values are private and iid. Using an indirect technique, we prove that it is always optimal to set the reserve price to the seller's own valuation. However, the maxmin reserve price may not be unique. Sometimes it is optimal to choose a deterministic reserve price even when randomization is allowed, which is unusual for maxmin settings. A second-price auction with the reserve equal to seller's value is an asymptotically optimal mechanism (among all ex post individually rational mechanisms) as the number of bidders grows without bound.

Second-Price Auctions with Private Entry Costs

We study asymmetric second-price auctions under incomplete information. The bidders have two potentially different, commonly known, valuations for the object and private information about their entry costs. The seller, however, does not benefit from these entry costs. We calculate the equilibrium strategies of the bidders and analyze the optimal design for the seller in this environment in terms of expected entry and the number of potential bidders.

Teams and individuals in standard auction formats: decisions and emotions

Our study compares individual and team bidding in standard auction formats: first-price, second-price and ascending-price (English) auctions with independent private values. In a laboratory experiment, we find that individuals overbid more than teams in first-price auctions and deviate more from bidding their own value in second-price auctions. However, we observe no difference in bidding behavior in English auctions. Based on control variables, we provide evidence that the observed difference could be explained by better reasoning abilities of teams. Emotions seem to play a role in determining bids, but the effect of emotions on bidding does not differ between individuals and teams.

Optimal Information Disclosure in Classic Auctions

We characterize the revenue-maximizing information structure in the second-price auction. The seller faces a trade-off: more information improves the efficiency of the allocation but creates higher information rents for bidders. The information disclosure policy that maximizes the revenue of the seller is to fully reveal low values (where competition is high) but to pool high values (where competition is low). The size of the pool is determined by a critical quantile that is independent of the distribution of values and only dependent on the number of bidders. We discuss how this policy provides a rationale for conflation in digital advertising. (JEL D44, D82, D83, M37)

Traffic management and resource allocation for UAV-based parcel delivery in low-altitude urban space

This research proposes a framework of Unmanned Aircraft Vehicles (UAV) system traffic management in the context of parcel delivery in low-altitude urban airspace, including clustering-based UAV path planning, Unmanned Aircraft System Traffic Management (UTM) with conflict detection and resolution (CD&R), and mechanism design for airspace resource allocation. For UAV path planning, we develop a procedure by first clustering a large variety of obstacles that arise from building heights and terrain topology and can impede UAV flying. Based on the clustered obstacles, Saturated Fast-Marching Square (Saturated FM2) algorithm is then employed to generate optimal and alternative paths for each UAV mission. While identifying the optimal and alternative paths does not consider UAV traffic interactions, several traffic management models are proposed to efficiently allocate spatial and temporal airspace resources to UAV missions. The UTM models determine the departure time and the path to take for each UAV flight while resolving path conflicts from different perspectives. Specifically, four UTM models are proposed: Sequential Delay (SD) Model, Sequential Delay/Reroute (SDR) Model, Full Optimization (FO) Model, and Batch Optimization (BO) Model. Among the four models, the BO model is of particular interest as it strikes a balance between seeking a system optimum solution and maintaining computational tractability. Given that traffic management requires private information from UAV operators, the Vickrey-Clarke-Groves (VCG) mechanism is further adapted to the UTM context, in which airspace resource allocation is performed in conjunction with a payment scheme to incentivize truthful private information reporting by UAV operators. Extensive numerical analysis is conducted with San Francisco as the case study area. The results show the effectiveness of the proposed framework, particularly the scalability of the BO model. We also find that payment by a UAV flight under the adapted VCG mechanism depends critically on traffic density and the extent of interaction the UAV flight has with other flights.

A Hybrid Price Auction-Based Secure Routing Protocol Using Advanced Speed and Cosine Similarity-Based Clustering against Sinkhole Attack in VANETs.

In ad-hoc vehicle networks (VANETs), the random mobility causes the rapid network topology change, which leads to the challenge of the reliable data transmission. In this paper, we propose a hybrid-price auction-based secure routing (HPA-SR) protocol using advanced speed and cosine similarity-based (ASCS) clustering to establish a secure route to avoid sinkhole attacks and improve connectivity between nodes. The main features and contributions of the proposed HPA-SR protocol are as follows. First, the HPA-SR protocol is employed by the first- and second-price auctions to avoid sinkhole attacks. More specifically, using the Markov decision process (MDP), each node can select a kind of auction method to establish the secure route by avoiding the sinkhole attack. Second, the advanced speed cosine similarity clustering protocol that is considered as underlying structure is presented to improve the connectivity between nodes. The ASCS is constructed based on the cosine similarity and distance between nodes using the speed and direction of the nodes. The results of the performance show that the proposed HPA-SR protocol can establish the secure route avoiding the sinkhole attack while the proposed ASCS clustering can support the strong connectivity. Besides, the HPA-SR with ASCS protocol can show better performance than the benchmark protocol in terms of the routing delay, packet loss ratio, number of packet loss, and control overhead.

Setting Reserve Prices in Second-Price Auctions with Unobserved Bids

In this work we consider a seller who sells an item via second-price auctions with a reserve price. By controlling the reserve price, the seller can influence the revenue from the auction, and in this paper, we propose a method for learning optimal reserve prices. We study a limited information setting where the probability distribution of the bids from bidders is unknown and the values of the bids are not revealed to the seller. Furthermore, we do not assume that the seller has access to a historical data set with bids. Our main contribution is a method that incorporates knowledge about the rules of second-price auctions into a multiarmed bandit framework for optimizing reserve prices in our limited information setting. The proposed method can be applied in both stationary and nonstationary environments. Experiments show that the proposed method outperforms state-of-the-art bandit algorithms. In stationary environments, our method outperforms these algorithms when the horizon is short and performs as good as they do for longer horizons. Our method is especially useful if there is a high number of potential reserve prices. In addition, our method adapts quickly to changing environments and outperforms state-of-the-art bandit algorithms designed for nonstationary environments. Summary of Contribution: A key challenge in online advertising is the pricing of advertisements in online auctions. The scope of our study is second-price auctions with a focus on the reserve price optimization problem from a seller’s point of view. This problem is motivated by the real-life practice of small and medium-sized web publishers. However, the proposed solution approach is applicable to any seller who sells an item via second-price auctions and wants to optimize its reserve price during these auctions. Our solution approach is based on techniques from machine learning and operations research, and it would be beneficial especially for sellers who start the selling process without any historical data and can collect the data on the outcomes of the auctions while making reserve price decisions over time. History: Accepted by RamRamesh, Area Editor for Data Science &amp; Machine Learning. Supplemental Material: The supplementary material is available at https://doi.org/10.1287/ijoc.2022.1199 .

Comparison of Four Basic Types of Auctions

Auction is a good way for people to exchange their goods and services and is essential to our daily life. Auctions can be classified into various genres and kinds depending on their unique rules. In this essay, I focused mainly on the four basic kinds of auctions: First-Price sealed-bid auction, Second-Price sealed-bid auction, Ascending-bid auction and descending-bid auction. I also tried to use several simple models to find out the characteristics and optimal strategies for each of the auction. Having their own advantages and weakness, different auctions should be used depending on specific situations to further maximize the efficiency of the auctions.

Applications of Game Theory in Microeconomics

Game theory has been used as a potent analytical tool by numerous areas since its inception. It has been more popular in microeconomic analysis in recent years. It is not an exaggeration to claim that it completely rewrites microeconomics. The major ideas of game theory are summarized in this paper, as well as their application in microeconomics. This study examines the three elements and key types of game theory in its fundamental material. The Nash equilibrium and other equilibria expanded by Nash equilibrium are then reviewed in game theory equilibrium. Then, the Cournot model, Stackelberg model, and Bertrand model are discussed in game theory and market analysis. Finally, in the section on game theory and auction, it explained that, within the context of the game, English auctions and second-price sealed-bid auctions should use comparable strategies, however Dutch auctions and first-price sealed-bid auctions should conceal their own valuations.

The Strange Role of Information Asymmetry in Auctions—Does More Accurate Value Estimation Benefit a Bidder?

We study the second-price auction in which bidders have asymmetric information regarding the item’s value. Each bidder’s value for the item depends on a private component and a public component. While each bidder observes their own private component, they hold different and asymmetric information about the public component. We characterize the equilibrium of this auction game and study how the asymmetric bidder information affects their equilibrium bidding strategies. We also discover multiple surprisingly counter-intuitive equilibrium phenomena. For instance, a bidder may be better off if she is less informed regarding the public component. Conversely, a bidder may sometimes be worse off if she obtains more accurate estimation about the auctioned item. Our results suggest that efforts devoted by bidders to improve their value estimations, as widely seen in today’s online advertising auctions, may not always be to their benefit.

Bid outcome processing in Vickrey auctions: An ERP study.

Online retailers often sell products using a socially competitive second-price sealed-bid auction known as a Vickrey auction (VA), an incentivized demand-revealing mechanism used to elicit players' subjective values. The VA presents a situation of risky decision-making, which typically implements value processing and a loss aversion mechanism. Neural outcome processing of VA bids are not known; this study explores this for the first time using EEG. Twenty-eight healthy participants bid on household items against an anonymous, computerized opponent. Bid outcome event-related potentials were predicted to differentiate between three conditions: outbid (no-win), large margin win (bargain), and small margin win (snatch). Individual loss aversion values were evaluated in a separate behavioral experiment offering gains or losses of variable amounts but equal chances against an assured gain. Processing outcomes of VA bids were associated with a feedback-related negativity (FRN) potential with a spatial maximum at the vertex (251-271 ms), where bargain win trials resulted in greater FRN amplitudes than snatch win trials. Additionally, a P300 potential was sensitive to win versus no-win outcomes and to retail price. Individual loss aversion level did not correlate with the strength of FRN or P300. Results show that outcome processing in a VA is associated with FRN that differentiates between relatively advantageous and less advantageous gains, and a P300 that distinguishes between the more and less expensive auction items. Our findings pave the way to an objective exploration of economic decision-making and purchasing behavior involving a widely popular auction.

Ordering properties of the second smallest and the second largest order statistics from a general semiparametric family of distributions

In this article, we consider the second smallest and the second largest order statistics from a general semiparametric family of distributions. The fail-safe system, the second-price sealed-bid auction, the second-price reversed auction are some classic examples where these order statistics are used. Here, we derive some stochastic comparisons results for these order statistics. Further, we show that the developed results hold for many well-known semiparametric models, namely, proportional hazard and reversed rates models, scale model, and proportional odds model.

Auctions: A New Method for Selling Objects with Bimodal Density Functions

In this paper we define a new auction, called the Draw auction. It is based on the implementation of a draw when a minimum price of sale is not reached. We find that a Bayesian Nash equilibrium is reached in the Draw auction when each player bids his true personal valuation of the object. Furthermore, we show that the expected profit for the seller in the Draw auction is greater than in second-price auctions, with or without minimum price of sale. We make this affirmation for objects whose valuation can be modeled as a bimodal density function in which the first mode is much greater than the second one. Regarding the Myerson auction, we show that the expected profit for the seller in the Draw auction is nearly as good as the expected profit in the optimal auction, with the difference that our method is much more simple to implement than Myerson’s one. All these results are shown by computational tests, for whose development we have defined an algorithm to calculate Myerson auction.

Antimonopoly regulation method in energy markets based on the Vickrey–Clarke–Groves mechanism

A profit-maximizing producer with market power operating a portfolio of generating units at the centralized two-settlement energy market may submit not only the altered cost but also the distorted values of the technical parameters of its generating units, which enter both the producer's private constraints and the system-wide constraints of the centralized dispatch optimization problem. Prior research on the suitability of the generic Vickrey–Clarke–Groves (VCG) mechanism as an antimonopoly measure against such a producer focused on the distortion of the offered output cost only. We evaluate the applicability of the VCG mechanism against a producer that also misreports the technical parameters of its units. To ensure the applicability of the VCG method in this setting, we identify an additional assumption on the variations of the feasible set induced by alterations of the producer's technical parameters. In the framework of the VCG mechanism, we propose an antimonopoly regulation method based on a regulator estimate of the producer's truthful bid. The error in the estimate affects neither the producer's dominant bid nor its optimal nodal output but manifests itself in the total uplift payment (budget imbalance). This ensures optimality of dispatch and shields the (pre-uplift) market prices from the producer's market power.

Twofold multiprior preferences and failures of contingent reasoning

We propose a model of incomplete twofold multiprior preferences, in which an act f is ranked above an act g only when f provides higher utility in a worst-case scenario than what g provides in a best-case scenario. The model explains failures of contingent reasoning, captured through a weakening of the state-by-state monotonicity (or dominance) axiom. Our model gives rise to rich comparative statics results, as well as extension exercises, and connections to choice theory. We present an application to second-price auctions.

Strategy and design of multi‐unit auction in grouped asymmetric setting

In this study, the difference amongst bidders is modelled by the two parameters of valuation and marginal utility. Thus, the symmetrical multi‐unit auction is extended to the asymmetric private value model. The optimal strategy of any different bidders can be solved by the model, which expands the practical application of multi‐unit auction theory. On this basis, the yield and price volatility of different auction mechanisms under the ‘two‐group case’ are evaluated. The results show that Vickrey auction is generally superior to uniform price auction. Different from the other two formats, the fluctuation range of discriminatory price auction revenue is large.

An efficient, open-bid procurement auction for small-scale electricity markets

Despite early calls to investigate the application of Vickrey auctions in electricity markets, academic literature still provides little insight into the matter. Similarly, despite general auction-theoretic literature discussing various advantages of employing revealed rather than sealed bidding procedures, publications on electricity market auctions rarely even mention differences between these opposing features. This paper marries these neglected features into a new auction model for electricity markets. We propose a novel open-bid, descending-clock auction capable of handling inter-bidder dependencies such as thermal line limits. A novel set of termination criteria ensures that our proposed auction facing markets with power balance and generator capacity constraints and thermal line limits, preserves truthful bidding as a dominant strategy, which, if employed by all bidders, allocates supply efficiently constituting an ex-post perfect equilibrium. Furthermore, we discuss known disadvantages of Vickrey–Clarke–Groves type auctions in the context of our proposed auction applied in electricity markets.

Automatically Improved VCG Mechanism for Local Energy Markets via Deep Learning

The proliferation of distributed renewable energy resources and plug-in electric vehicles (EVs) have helped residential electricity consumers evolve into prosumers as they participate in the local energy market (LEM) by engaging in transactions of surplus electricity. In this system, the budgetbalance problem is a frequent issue, particularly when Vickrey-Clarke-Groves (VCG)-based mechanisms are applied to managing the two-sided nature of LEM. Although this issue could be partially addressed by manually modifying the LEM, the variance in the LEM environment needs to be better understood. This paper proposes a deep learning-based automatic mechanism design (AMD) method to improve VCG for tackling the budget-balanced two-sided LEM, as a way to avoid tedious manual adjustments. A convolutional neural network (CNN) with self-attention mechanism is constructed to extract features from biddings and to provide robust generalization capabilities for participating prosumers. The gated recurrent units (GRUs) are utilized to extend the proposed approach to the non-stationary bidding environment. This improved mechanism is targeted as efficient and incentive compatible, with the ability to keep the balance between the budget-balance and individual rationality. Case studies are conducted to demonstrate effectiveness of the proposed automatically improved mechanism and adaptive ability to various bidding environments.

A diffusion mechanism for multi-unit commodity allocation in economic networks

In this research, we aim to minimise the total cost of procuring multi-units of commodities. In classical procurement paradigms, the buyer is only aware of a limited number of sellers. This limited participation of sellers might lead to drop-in competition, which in turn, leads to higher procurement cost. In this regard, we propose a novel decentralised group commodity allocation approach. The proposed approach introduces an information diffusion based dual-bid procurement auction mechanism. This mechanism incentivises the participating sellers to report their valuations truthfully. Also, it encourages them to spread the procurement information to other neighbouring sellers. As a result, the proposed mechanism helps each buyer to reach out to the distant sellers and procure the required amount of commodities at the minimum possible price. Additionally, the proposed mechanism intends to give fair chances to the distant sellers to participate in the procurement auction. Finally, we prove that the proposed mechanism is incentive-compatible and individually rational. Besides, we also show that the proposed mechanism has a lower procurement cost than the direct extension of the Vickrey-Clarke-Groves (VCG) mechanism.