Discriminatory Price Auctions Research Articles

Information Spillovers and Sovereign Debt: Theory Meets the Eurozone Crisis

Abstract We develop a theory of information spillovers in sovereign bond markets in which investors can learn about default risk before trading in primary and secondary markets. If primary markets are structured as multi-unit discriminatory-price auctions, an endogenous winner’s curse leads to strategic complementarities in information acquisition. Shocks to default risk in one country may trigger crisis episodes with widespread information acquisition, sharp increases in the level and volatility of yields in risky countries, low and stable yields in safe countries, market segmentation, and arbitrage profits between primary and secondary markets. These predictions are consistent with the dynamics of auction informativeness during the Eurozone Sovereign Debt Crisis, which we measure using the reaction of secondary market yields to primary market yields.

Auction Mechanisms and Treasury Revenue: Evidence from the Chinese Experiment

This paper exploits a large-scale auction experiment conducted by two Chinese government treasury security issuers—the Chinese Development Bank and the Export-Import Bank—to investigate whether treasury securities should be sold through uniform price or discriminatory price auction mechanisms. Based on the outcomes of more than 300 treasury securities issued through an alternating auction-rule market experiment, we find that yield rates of the two auction formats are not statistically different. Further, these estimates indicate there is no significant economic difference in terms of revenue between the two auction mechanisms. This result is robust across different bond yield-rate measurements and participation behavior. (JEL D44, E63, G12, O16, P34)

Impact of Forecasting Models Errors in a Peer-to-Peer Energy Sharing Market

The use of energy sharing models in smart grids has been widely addressed in the literature. However, feasible technical solutions that can deploy these models into reality, as well as the correct use of energy forecasts are not properly addressed. This paper proposes a simple, yet viable and feasible, solution to deploy energy management systems on the end-user-side in order to enable not only energy forecasting but also a distributed discriminatory-price auction peer-to-peer energy transaction market. This work also analyses the impact of four energy forecasting models on energy transactions: a mathematical model, a support-vector machine model, an eXtreme Gradient Boosting model, and a TabNet model. To test the proposed solution and models, the system was deployed in five small offices and three residential households, achieving a maximum of energy costs reduction of 10.89% within the community, ranging from 0.24% to 57.43% for each individual agent. The results demonstrated the potential of peer-to-peer energy transactions to promote energy cost reductions and enable the validation of auction-based energy transactions and the use of energy forecasting models in today’s buildings and end-users.

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.

The Performance of a Repeated Discriminatory Price Auction for Ecosystem Services

The Performance of a Repeated Discriminatory Price Auction for Ecosystem Services

Property rights in the Crypto age: NFTs and the auctioning of limited edition artwork

Non-fungible tokens (NFTs) on blockchains have recently emerged as a means of certifying the originality of digital properties, such as artwork. In this paper, we examine limited-edition auctions for the sale of digital artwork using NFTs. We study two types of limited-edition auctions that have been used in practice: the `silent' and `ranked' auctions. We argue that the silent limited-edition auction as currently used in NFT markets is a variant of the well-known discriminatory price auction. We derive the Bayesian Nash equilibrium of this auction, and show that it is revenue equivalent to a VCG auction. Our analysis suggests that bidding behavior in a silent limited-edition auction is more aggressive than a standard discriminatory price auction without editioning; consequently, equilibrium bids are higher in the former. We also study the generalized English auction as an outcome equivalent auction to the ranked limited-edition auction, and show that this does not have a truthful equilibrium. Finally, we examine the uniform-price auction as a potential alternative mechanism for conducting an auction with editioning, and establish the absence of a truthful equilibrium in this instance as well. Our paper represents one of the first attempts to formally model the allocation of property rights using auctions in the digital environment, which is at the forefront of current innovation.

Mixed Mechanisms for Auctioning Ranked Items

This paper deals with the problem of designing and choosing auctioning mechanisms for multiple commonly ranked objects as, for instance, keyword auctions in search engines on Internet. We shall adopt the point of view of the auctioneer who has to select the auction mechanism to be implemented not only considering its expected revenue, but also its associated risk. In order to do this, we consider a wide parametric family of auction mechanisms which contains the generalizations of discriminatory-price auction, uniform-price auction and Vickrey auction. For completeness, we also analyze the Generalized Second Price (GSP) auction which is not in the family. The main results are: (1) all members of the family satisfy the four basic properties of fairness, no over-payment, optimality and efficiency, (2) the Bayesian Nash equilibrium and the corresponding value at risk for the auctioneer are obtained for the considered auctions, (3) the GSP and all auctions in the family provide the same expected revenue, (4) there are new interesting auction mechanisms in the family which have a lower value at risk than the GSP and the classical auctions. Therefore, a window opens to apply new auction mechanisms that can reduce the risk to be assumed by auctioneers.

Multi-unit multiple bid auctions in balancing markets: An agent-based Q-learning approach

There is an ongoing debate on the appropriate auction design for competitive electricity balancing markets. Uniform (UPA) and discriminatory price auctions (DPA), the prevalent designs in use today, are assumed to have different properties with regard to prices and efficiencies. These properties cannot be thoroughly described using analytical methods due to the complex strategy space in repeated multi-unit multiple bid auctions. Therefore, using an agent-based Q-learning model, we simulate the strategic bidding behaviour in these auctions under a variety of market conditions. We find that UPAs lead to higher prices in all analysed market settings. This is mainly due to the fact that players engage in bid shading more aggressively. Moreover, small players in UPAs learn to free ride on the price setting of large players and earn higher profits per unit of capacity owned, while they are disadvantaged in DPAs. UPAs also generally feature higher efficiencies, but there are exceptions to this observation. If demand is varying and players are provided with additional information about scarcity in the market, market prices increase only in case asymmetric players are present.

Evaluating the Potential Contribution of Multi-Attribute Auctions to Achieve Agri-Environmental Targets and Efficient Payment Design

This paper analyses the performance of a multi-attribute auction for securing agri-environmental outcomes and cost-effective agri-environmental payments (AEPs). We set up a discriminatory price auction model in which farmers make an offer based on two attributes (i.e. the AEP and a proxy of environmental outcome). We provide a numerical simulation for a hypothetical agri-environmental scheme (AES) in Italy using FADN data 2011 for the Emilia-Romagna region (E-R). In three implementation scenarios, we compare the Budgetary cost-effectiveness (BCE), the Economic cost-effectiveness (ECE) and Information rent (IR) of the auction with that of two alternative policy instruments (i.e. uniform payment and marginal flat rate payment). Due to the heterogeneity in bidders' opportunity costs, the auction is more cost-effective than a uniform payment in delivering the target outcome. The performance indicators are sensitive to the farmers' expectations about the bid caps, revealing the opportunity of using both competition effect and information leverage associated with the implementation mechanism to increase the auction outcome when the budget is limited.

Discriminatory price auctions with resale and optimal quantity caps

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 results on first‐price auctions with resale to this setting and use these results to give a tractable characterization of equilibrium behavior. We use this characterization to study the policy of capping the amount that may be won by large bidders in the auction, a policy that 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 welfare or revenue can have contradictory implications for the choice of cap.

Designing cost-efficient payments for forest-based carbon sequestration: An auction-based modeling approach

Conservation auctions can reveal information about the opportunity costs of afforestation, which can be combined with the carbon sequestration benefits of land-use changes to design cost-efficient payment systems. Furthermore, the impact of integrating cost-benefit information to ensure efficiency gains or to ensure minimal efficiency losses in multi-round conservation auctions, where landowners learn to extract information rents, depends on the level of correlation between costs and benefits. Incorporating discriminatory-price auction theory, and an agent-based model, simulated data are used to examine the cost-efficiency of cost-ranked and cost-benefit-ranked auction-based payment designs for forest-based carbon storage for alternative levels of correlation between afforestation opportunity costs and carbon sequestration capacities in static and dynamic settings. Results show that the cost-benefit-ranked design is more cost-efficient than the cost-ranked design in a static setting even though the relative spatial heterogeneities of costs and benefits are identical. More importantly, the cost-efficiency of the cost-benefit-ranked design is generally robust to deterioration as bidders learn over repeated auction rounds, compared with the cost-ranked design, and more resistant to deterioration for some levels of correlation.

The behaviour of bidders in quantitative-easing auctions of sovereign bonds in Japan: Determinants of the popularity of the 9 to 10-year maturity segment

This article provides Japanese evidence on how bidders behaved in multiple-object, multiple-unit, discriminatory-price auctions. It does so by analysing the popularity of the 9 to 10-year maturity segment in the Bank of Japan’s auction purchases of government bonds with remaining maturities of 5–10 years over the period 2013–2015 in its Quantitative Easing policy. The popularity had five determinants: (i) a morning-market factor, the relative interest-rate changes in the morning for the 10-year maturity length compared to 5 to 9-year maturity lengths, (ii) a volatility factor, the relative volatility of 10-year interest rates compared to the other maturity lengths, (iii) a yield-curve factor, the relative value of 10-year interest rates compared to 7-year ones, (iv) a market-liquidity factor, the relative liquidity level for current 10-year government bonds compared to those with 7-year remaining maturity, and (v) a scarcity factor, the size of the auctions relative to the amount of marketable government bonds in the 9 to 10-year maturity segment. The popularity also co-integrated with the five factors, amongst which the yield-curve factor was the most powerful in explaining the popularity’s long-term equilibria. It took three auctions for the popularity to reach a new equilibrium, after diverting by five percentage points from its long-term equilibrium. The morning-market factor was the greatest source of unexpected changes in the popularity.

Efficient and optimal mechanisms with radio spectrum sharing

Optimal mechanism design with spectrum sharing differs from the traditional setting mainly in that some technological constraints (e.g., non-interference constraints) need to be taken into account explicitly. In this paper we characterize surplus-maximizing (efficient) and revenue-maximizing (optimal) mechanisms in a spectrum sharing context where a principal allocates transmitted power among a group of potentially interested users (transmitter-receiver pairs). Under regularity conditions about value distributions and non-interference constraints, we show that efficiency (optimality) typically involves spectrum sharing by multiple users, and the exact allocation of transmitted power is determined such that the ratio of marginal value (virtual value) over marginal cost (in terms of the cost to the interference generated) is equal among all shared users. We show that efficient and optimal mechanisms in our setting are actually dominant-strategy incentive compatible, and that they can also be implemented by well-designed all-pay or discriminatory-price auctions.

A Walrasian Theory of Sovereign Debt Auctions with Asymmetric Information

How does investors' information about a country's fundamentals, and the fact that this information may be asymmetrically held, affect a country's financing cost? Motivated by this question, and by the observation that sovereign bonds are usually auctioned in large lots to a large number of potential investors, we develop a novel model of auctions with asymmetric information that relies on price-taking and rational expectations. We first characterize sovereign bond prices for different degrees of asymmetric information under two commonly-used protocols: discriminatory-price auctions and uniform-price auctions. We show that there is trade-off between these protocols if information is sufficiently asymmetric: expected bond yields are higher when pricing is discriminatory, but yield volatility is higher when pricing is uniform. We then study endogenous information acquisition and find that (i) discriminatory auctions may display multiple welfare-ranked informational equilibria, and (ii) investors are less likely to acquire information in uniform auctions.

Bidding Behavior in Multi-Unit Auctions with Asymmetric Bidders

This paper compares equilibrium bidding strategies in the discriminatory-price auction (DPA) and the uniform-price auction (UPA) when at least two identical and indivisible units of a good sold to a multi-unit bidder (i.e., with demand for two units of the good) and a set of single-unit bidders. We show that when the multi-unit bidder confronts a set of stronger (resp. weaker) single-unit competitors in term of the likelihood ratio dominance in valuations, she is inclined to submit more (resp. less) aggressive bids for both units in the DPA, whereas she is more likely to shade her bids for the second unit in the UPA when her valuation of the second unit is above a threshold for nonzero bids.

How well do conservation auctions perform in achieving landscape-level outcomes? A comparison of auction formats and bid selection criteria

This paper studies the performance of auction design features regarding pricing mechanisms and bid selection criteria for securing wildlife zones across different holdings. We compare two pricing mechanisms: a discriminatory-price auction and a uniform-price ascending auction, and four bid selection criteria on the basis of: total bid, bid-per-value ratio, bid-per-area ratio and a mixed criterion where bids are formed on the basis of cost but they are selected based on the bid-per-value ratio. We develop a best-response group-bidding model for a discriminatory-price auction where bidders form optimal group bids for individual wildlife zones. In the uniform-price ascending auction, individual landholders respond to prices, which are successively raised by the auctioneer and whenever all the landholders from a single zone agree to participate (i.e. the first zone is formed), the auction stops. Based on numerical simulations using a bio-economic model of malleefowl conservation, we observe that the discriminatory-price auction is more cost-effective than the uniform-price ascending auction. However, the budgetary cost-effectiveness of a discriminatory-price auction is sensitive to bidder uncertainty about the number of competing bidder groups and the highest cost of establishing a wildlife zone among these groups. In terms of bid selection, the mixed bid selection criterion performs best. We discuss the policy implications of these findings.

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.

The Effect of Information on Discriminatory-Price and Uniform-Price Reverse Auction Efficiency: An Experimental Economics Study of the Purchase of Ecosystem Services

The Effect of Information on Discriminatory-Price and Uniform-Price Reverse Auction Efficiency: An Experimental Economics Study of the Purchase of Ecosystem Services

Auction Performance in Wholesale Electricity Markets in the Presence of Transmission Constraints and Transmission Costs

Electricity markets are becoming more integrated around the world. However, the knowledge of the effects of different auction formats on suppliers' strategies in the presence of transmission constraints and transmission costs is still very limited. In this paper, I analyze the performance of uniform and discriminatory price auctions in the presence of transmission constraints and transmission costs. When the transmission capacity is binding, the discriminatory price auction could outperform the uniform price auction, minimizing the equilibrium price and the transmission costs. Moreover, when the transmission capacity is binding, an increase in transmission costs could be pro-competitive when the auction is discriminatory, but not when the auction is uniform.

An Empirical Test of Auction Efficiency: Evidence from MBS Auctions of the Federal Reserve

Auction theory has ambiguous implications regarding the relative efficiency of three formats of multiunit auctions: uniform-price, discriminatory-price, and Vickrey auctions. We empirically evaluate the performance of these three auction formats using the bid-level data of the Federal Reserve's purchase auctions of agency mortgage-backed securities (MBS) from June 1, 2014 through November 17, 2014. We estimate marginal cost curves for all dealers, at each auction, based on structural models of the multiunit discriminatory-price auction. Our preliminary results suggest that neither uniform-price nor Vickrey auctions outperform discriminatory-price auctions in terms of the total expenditure. However, they do outperform in terms of efficiency, with efficiency gains around 0.74% of the surplus that dealers extract. We caution that our empirical estimation and analysis involve technical assumptions made about the specific auction mechanism the Federal Reserve uses and how auction participants perceive the auction mechanism, both of which may be distinct from practice and may alter the conclusions substantively.