Asymmetric Auctions Research Articles

Asymmetric auctions: Perturbations, ε- equilibrium, and equilibrium

We consider first-price auctions with independent and private valuations that have asymmetric valuation distributions and supports. We first show the existence of equilibrium in these auctions through a perturbation approach, thereby establishing that the limit of Bayesian Nash equilibria (BNE) of such perturbed auctions is indeed the Bayesian Nash equilibrium (BNE) of the limit auction with asymmetric supports. We then characterize this BNE and show that the ε-equilibrium (ε-BNE) of the auction with asymmetric supports is a BNE of “close” auctions with common supports. We then demonstrate some numerical examples.

Virtue of Simplicity in Asymmetric Auctions

Virtue of Simplicity in Asymmetric Auctions

Learning Equilibria in Asymmetric Auction Games

Computing Bayesian Nash equilibrium strategies in auction games is a challenging problem that is not well-understood. Such equilibria can be modeled as systems of nonlinear partial differential equations. It was recently shown that neural pseudogradient ascent (NPGA), an implementation of simultaneous gradient ascent via neural networks, converges to a Bayesian Nash equilibrium for a wide variety of symmetric auction games. Whereas symmetric auction models are widespread in the theoretical literature, in most auction markets in the field, one can observe different classes of bidders having different valuation distributions and strategies. Asymmetry of this sort is almost always an issue in real-world multiobject auctions, in which different bidders are interested in different packages of items. Such environments require a different implementation of NPGA with multiple interacting neural networks having multiple outputs for the different allocations in which the bidders are interested. In this paper, we analyze a wide variety of asymmetric auction models. Interestingly, our results show that we closely approximate Bayesian Nash equilibria in all models in which the analytical Bayes–Nash equilibrium is known. Additionally, we analyze new and larger environments for which no analytical solution is known and verify that the solution found approximates equilibrium closely. The results provide a foundation for generic equilibrium solvers that can be used in a wide range of auction games. History: Accepted by Ram Ramesh, Area Editor for Data Science & Machine Learning. Funding: This work was supported by Deutsche Forschungsgemeinschaft [Grant BI-1056/I-9]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.1281 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2021.0151 ) at ( http://dx.doi.org/10.5281/zenodo.7407158 ).

Effective Consensus-Based Distributed Auction Scheme for Secure Data Sharing in Internet of Things

In a traditional electronic auction, the centralized auctioneer and decentralized bidders are in an asymmetric structure, where the auctioneer has more ability to decide the auction result. This asymmetric auction structure is not fair to the participants and not suitable for data auctions in the Internet of Things (IoT). The blockchain-based auction system, with participant equality and fairness, is typically symmetrical and particularly suitable for IoT data sharing. However, when applied to IoT data sharing in reality, it faces privacy and efficiency problems. In this context, how to guarantee privacy and break the inherent performance bottleneck of blockchain is still a major challenge. In this paper, a consensus-based distributed auction scheme is proposed for data sharing, which enforces privacy preservation and collusion resistance. A reverse auction-based decentralized data trading model is introduced to solve the trust problem without a centralized auctioneer, where bidders reach consensus on the auction result. Specifically, we devise a differentially private auction mechanism to incentivize data owners to participate in data sharing. An effective hybrid consensus algorithm is constructed among bidders to reach consensus on the auction result with improved security and efficiency. Theoretical analysis shows that the proposed scheme ensures the properties of privacy preservation, incentive compatibility and collusion resistance. Experimental results reveal that the proposed mechanism guarantees the data sharing efficiency and has certain scalability.

Efficiency in asymmetric auctions with endogenous reserve prices

In the standard independent private values model, the second-price auction (SPA) is generally taken to be more efficient than the first-price auction (FPA) when bidders are asymmetric. However, this conclusion assumes that reserve prices are identical across auctions. This paper endogenizes the reserve price and shows that it may be lower in the FPA. Hence, gains from trade are realized more often in the FPA. This effect may make the FPA more efficient than the SPA. Indeed, the FPA may Pareto dominate the SPA. That is, the FPA may be more profitable and yet be preferred by all bidders.

Numerical Solution of Asymmetric Auctions

We propose the backward indifference derivation (BID) algorithm, a new method to numerically approximate the pure strategy Nash equilibrium (PSNE) bidding functions in asymmetric first-price auctions. The BID algorithm constructs a sequence of finite-action PSNE that converges to the continuum-action PSNE by finding where bidders are indifferent between actions. Consequently, our approach differs from prevailing numerical methods that consider a system of poorly behaved differential equations. After proving convergence (conditional on knowing the maximum bid), we evaluate the numerical performance of the BID algorithm on four examples, two of which have not been previously addressed.

A First-Price Sealed-Bid Asymmetric Auction When Two Bidders Have Respective CRRA and General Utility Functions

We study a first-price auction with two bidders where one bidder is characterized by a constant relative risk aversion utility function (i.e., a concave power function) while the other has a general concave utility function. We establish the existence and uniqueness of the optimal strategic markups and analyze the effects of one bidder’s risk aversion level on the optimal strategic markups of him and his opponent’s, the allocative efficiency of the auction, and the seller’s expected revenue, respectively.

Ranking reversals in asymmetric auctions

This paper compares the first-price auction and the second-price auction with several asymmetric bidders who are either weak or strong. The ranking of these auctions in terms of profit may flip as the exogenous reserve price or the number of weak or strong bidders change. Similarly, with endogenous reserve prices the ranking may depend on the seller’s own-use valuation. In other words, the ranking may be fragile to changes along these dimensions. Existing models rule out such ranking reversals by imposing substantial structure on type distributions. The current paper relies on simple mechanism design arguments that require less structure.

How Subsidies Affect Asymmetric Procurement Auctions: Comparing Experimental Results to Theory

The use of bid preference auctions, where one class of bidders is offered favored treatment over another class, has received mixed attention in the literature. Research has shown there is an economic benefit of such policies thanks to lower costs for procurement auction buyers as incentives are offered to disadvantaged sellers. In this paper, we study one type of preferential procurement auction: the subsidy. Using a set of controlled experiments, we compare actual bidder behavior to what is predicted in equilibrium. We find that sellers suffer from overly aggressive bidding (but do learn over time). More importantly, we explore the behaviors that may explain any deviations from theory – focusing on best response bidding and what directional learning theory would predict based on prior round outcomes. We find evidence of myopic behaviors among bidders. One intriguing take-away is that cost-advantaged bidders may be more responsive to opponents’ bids. Due to the wide use of bid preference auctions to support both policy and social aims, our findings have both financial and societal implications.

Identification of Auction Models Using Order Statistics

Auction data often contain information on only the most competitive bids as opposed to all bids. The usual measurement error approaches to unobserved heterogeneity are inapplicable due to dependence among order statistics. We bridge this gap by providing a set of positive results. First, we show that symmetric auctions are identifiable using three consecutive order statistics or two consecutive ones with an instrument. Second, we introduce competition intensity, i.e., the number of bidders, as additional unobserved heterogeneity. Third, we extend our results to asymmetric auctions. Lastly, we apply our methods to U.S. Forest Service timber auctions and find that ignoring unobserved heterogeneity reduces both bidder and auctioneer surplus.

How Accurately Do Structural Asymmetric First-Price Auction Estimates Represent True Valuations?

Abstract Structural asymmetric first-price auction estimation methods have provided numerous empirical studies. However, due to the latent nature of underlying valuations, the accuracy of estimates is not feasibly testable with field data, a fact that could inhibit empirical auction market designs and applications based on structural estimates. To assess their accuracy, we provide an analysis of estimates derived from experimental asymmetric auction data, in which researchers observe valuations. We test the null of statistical equivalence between the estimated and true value distributions against the alternative of non-equivalence. When advanced models are used, the Modified Kolmogorov-Smirnov test fails to reject the distributional equivalence, supporting structural asymmetric auction estimations for auction market studies. In addition, recovered efficiencies have plus-minus 2.5 percent precision, compared to the true efficiencies.

Shapley-Folkman-Lyapunov theorem and Asymmetric First price auctions

Abstract In this paper non-convexity in economics has been revisited. Shapley-Folkman-Lyapunov theorem has been tested with the asymmetric auctions where bidders follow log-concave probability distributions (non-convex preferences). Ten standard statistical distributions have been used to describe the bidders’ behavior. In principle what is been tested is that equilibrium price can be achieved where the sum of large number non-convex sets is convex (approximately), so that optimization is possible. Convexity is thus very important in economics.

Assessment of Collusion Damages in First Price Auctions

We propose a structural method for estimating the revenue losses associated with bidding rings in symmetric and asymmetric first-price auctions. It is based on the structural analysis of auction data and is consistent with antitrust damage assessment methodologies: we build a but-for (competitive) scenario and estimate the differences between the two scenarios. We show in a Monte Carlo exercise that our methodology performs very well in moderate size samples. We apply it to Ohio Milk Data Set analyzed by Porter and Zona (1999) and find that damages are around 7%. Damages can be assessed without any information about unaffected markets.

Costly Entry and the Optimality of Asymmetric Auction Designs

We analyze optimal auction mechanisms when bidders base costly entry decisions on their valuations, and bidders pay with a fixed royalty rate plus cash. With sufficient valuation uncertainty relative to entry costs, the optimal mechanism features asymmetry so that bidders enter with strictly positive but different (ex-ante) probabilities. When bidders are ex-ante identical, higher royalty rates—which tie payments more closely to bidder valuations—increase the optimal degree of asymmetry in auction design, further raising revenues. When bidders differ ex-ante in entry costs, the seller favors the low cost entrant; whereas when bidders have different valuation distributions, the seller favors the weaker bidder if entry costs are low, but not if they are high. Higher royalty rates cause the seller to favor the weaker bidder by less, and the strong bidder by more.

Sequential Bidding in Asymmetric First Price Auctions

AbstractWe study asymmetric first price auctions in which bidders place their bids sequentially, one after the other and only once. We show that, when bidders’ values are drawn from uniform distributions and are asymmetric, i.e., there is a strong bidder and a weak bidder (the strong bidder’s distribution first order stochastically dominates that of the weak bidder’s), the expected revenue in the sequential bidding first price auction (when the strong bidder bids first) may be higher than in the simultaneous bidding first price auction as well as the simultaneous bidding second price auction. The expected payoff of the weak bidder is also higher in the sequential first price auction. Therefore a seller interested in increasing revenue facing asymmetric bidders may find it beneficial to order them and let them bid sequentially instead of simultaneously.

Asymmetric Auctions with Endogenous Participation

We study endogenous participation in asymmetric second price auctions where one bidder is special. We show seller revenue decreases whenever the special bidder becomes more dominant in the sense of FOSD, or more generally whenever the other bidders' profits are reduced. We also establish an equivalence result for second price auctions - any arbitrary distribution of the special bidder's value is competitively equivalent to one that is a power function of the value distribution of the other bidders. Finally, we analyze first-price auctions numerically and show that our results extend to this alternate mechanism.

Revenue Equivalence of Large Asymmetric Auctions

One of the most important results in auction theory is that when bidders are symmetric (homogeneous), then under quite general conditions, the seller's expected revenue is independent of the auctio...

Optimal Quantity Caps in Discriminatory Price Auctions with Resale

We present a model of a discriminatory price auction in which a large bidder competes against many small bidders, followed by a post-auction resale stage in which the large bidder is endogenously determined to be a buyer or a seller. We extend the first-price auction with resale results of Hafalir and Krishna (2008) to this setting and give a tractable characterization of equilibrium behavior. We use this to study the policy of capping the amount that may be won by large bidders in the auction. Despite being used in the US Treasury auction among others, this policy has received little attention in the auction literature. Our analysis shows that the trade-offs involved when adjusting these quantity caps can be understood in terms familiar to students of asymmetric first-price single unit auctions. Furthermore, whether one seeks to maximize revenue or efficiency has stark and contradictory implications for the choice of cap.

Scalable Games: Modelling Games of Incomplete Information

We provide conditions to allow modelling situations of asymmetric information in a tractable manner. In addition, we show a novel relationship between certain games of asymmetric information and corresponding games of symmetric information. This framework establishes links between certain games separately studied in the literature. The class of games considered is defined by scalable preference relations and a scalable information structure. We show that this framework can be used to solve asymmetric contests and auctions with loss aversion.

Revenue Equivalence of Large Asymmetric Auctions

The paper analyzes the revenue of auctions with asymmetric bidders with a large, but finite number of players. We explicitly calculate the seller’s expected revenue in large asymmetric first-price, second-price, and optimal auctions to O(1/n 3) accuracy, where n is the number of players. These calculations show that the revenue differences among these three auction mechanisms scale as ∈2/n 3, where e is the level of asymmetry (heterogeneity) among the distributions of bidders’ valuations. This novel scaling law shows that bidders’ asymmetry already has a negligible effect on revenue ranking of auctions with several (e.g., n = 6) bidders. In contrast, previous results studied only the limiting case n → ∞. We also show that bidders’ asymmetry always reduces the expected revenue in large auctions, but not necessarily in small ones. Finally, we extend the asymptotic O(∈2/n 3) revenue equivalence to a broader class of asymmetric auctions.