Uniform Auction Research Articles

Collusion in Auctions for Emission Permits: An Experimental Analysis

Environmental markets have several institutional features that provide a new context for the use of auctions and which have not been studied previously. This paper reports on laboratory experiments testing three auction forms: uniform and discriminatory price sealed bid auctions and an ascending clock auction. We test the ability of subjects to tacitly or explicitly collude in order to maximize profits. Our main result is that the discriminatory and uniform price auctions produce greater revenues than the clock auction, both without and with explicit communication. The clock appears to be more subject to successful collusion because of its sequential structure and because it allows bidders to focus on one dimension of cooperation (quantity) rather than two (price and quantity).

Revenue Ranking of Discriminatory and Uniform Auctions with an Unknown Number of Bidders

An important managerial question is the choice of the pricing rule. We study whether this choice depends on the uncertainty about the number of participating bidders by comparing expected revenues under discriminatory and uniform pricing within an auction model with affiliated values, stochastic number of bidders, and linear bidding strategies. We show that if uncertainty about the number of bidders is substantial, then the discriminatory pricing generates higher expected revenues than the uniform pricing. In particular, the first-price auction might generate higher revenues than the second-price auction. Therefore, uncertainty about the number of bidders is an important factor to consider when choosing the pricing rule. We also study whether eliminating this uncertainty, i.e., revealing the number of bidders, is in the seller's interests, and discuss the existence of an increasing symmetric equilibrium.

Competing auctions with endogenous quantities

Two sellers decide on their discrete supply of a homogenous good. There is a finite number of buyers with unit demand and privately known valuations. In the first model, there is a centralized market place where a uniform auction takes place. In the second, there are two distinct auction sites, each with one seller, and buyers decide where to bid. Using the theory of potential games, we show that in the one-site auction model there is always an equilibrium in pure-strategies. In contrast, if the distribution of buyers values has an increasing failure rate, and if the marginal cost of production is relatively low, there is no pure-strategy equilibrium where both sellers make positive profits in the competing sites model. We also identify conditions under which an equilibrium with a unique active site exists. We deal with the finite and discrete models by using several results about order statistics developed by Richard Barlow and Frank Proschan [R. Barlow, F. Proschan, Mathematical Theory of Reliability, Wiley, New York, 1965; R. Barlow, F. Proschan, Inequalities for linear combinations of order statistics from restricted families, Ann. Math. Statist. 37 (1966) 1593–1601; R. Barlow, F. Proschan, Statistical Theory of Reliability and Life Testing, McArdle Press, Silver Spring, 1975].

Sequential vs. single-round uniform-price auctions

We study sequential and single-round uniform-price auctions with affiliated values. We derive symmetric equilibrium for the auction in which k 1 objects are sold in the first round and k 2 in the second round, with and without revelation of the first-round winning bids. We demonstrate that auctioning objects in sequence generates a lowballing effect that reduces the first-round price. Total revenue is greater in a single-round, uniform auction for k = k 1 + k 2 objects than in a sequential uniform auction with no bid announcement. When the first-round winning bids are announced, we also identify a positive informational effect on the second-round price. Total expected revenue in a sequential uniform auction with winning-bids announcement may be greater or smaller than in a single-round uniform auction, depending on the model's parameters.

LEARNING OLIGOPOLISTIC COMPETITION IN ELECTRICITY AUCTIONS

This paper addresses the problem of auction markets efficiency within the context of recently liberalized electricity markets. Two different auction mechanisms, i.e., the uniform and the discriminatory price setting rules, have been employed worldwide in designing electricity markets. In this paper, we study the relative efficiency of the two auction mechanisms in the framework of the learning-in-games approach. The behavior of electricity suppliers are modeled by means of an adaptive learning algorithm and the demand is assumed to be constant and inelastic, according to a common hypothesis in electricity market modeling. Computational experiments results are interpreted according game theoretical solutions, i.e., Nash equilibria and Pareto optima. Different economic scenarios corresponding to a duopoly and a tripoly competition with different level of demand are considered. Results show that in the proposed conditions, sellers learn to play competitive strategies, which correspond to Nash equilibria. Finally, this study establishes that, in the presented computational setting and economic scenarios, the discriminatory auction mechanism results more efficient than the uniform auction one.

A Reinforcement Learning Model to Assess Market Power Under Auction-Based Energy Pricing

Auctions serve as a primary pricing mechanism in various market segments of a deregulated power industry. In day-ahead (DA) energy markets, strategies such as uniform price, discriminatory, and second-price uniform auctions result in different price settlements and thus offer different levels of market power. In this paper, we present a nonzero sum stochastic game theoretic model and a reinforcement learning (RL)-based solution framework that allow assessment of market power in DA markets. Since there are no available methods to obtain exact analytical solutions of stochastic games, an RL-based approach is utilized, which offers a computationally viable tool to obtain approximate solutions. These solutions provide effective bidding strategies for the DA market participants. The market powers associated with the bidding strategies are calculated using well-known indexes like Herfindahl-Hirschmann index and Lerner index and two new indices, quantity modulated price index (QMPI) and revenue-based market power index (RMPI), which are developed in this paper. The proposed RL-based methodology is tested on a sample network

Multi-unit auction format design

Multi-unit auctions are powerful mechanisms for the allocation of numerous resources and production contracts. However, there is uncertainty about the best auction formats when multi-unit auctions are used because there are multiple equilibria and analytical descriptions of optimum strategies are intractable. Empirical studies are scarce and most experimental studies are restricted to two bidders and two units. This paper constructs an agent-based model of bidders to compare the performance of alternative procurement auction formats under circumstances where bidders submit continuous bid supply functions and learn over time to adjust their bids in order to improve their net incomes. The results provide some confirmation of analytical predictions but also indicate that the range of bidding strategies employed is richer than what the theory expects. Bidder coordination for higher prices is possible under both the Vickrey and uniform auctions, especially when the population is heterogeneous and competition low. Judged by budgetary measures, the discriminatory auction is the most expensive when rationing is tight, but this outcome is reversed when rationing is less stringent. Budgetary outcomes can be improved if the auction is organized among more homogeneous bidders.

The Relevance of a Choice of Auction Format in a Competitive Environment

We examine the relevance of an auction format in a competitive environment by comparing uniform and discriminatory price auctions with many bidders in a private values setting. We show that if the number of objects for sale is small relative to the number of bidders, then all equilibria of both auctions are approximately efficient and lead to approximately the same revenue. When the number of objects for sale is proportional to the number of bidders, then the particulars of the auction format matter. All equilibria of the uniform auction are efficient, while all of the equilibria of the discriminatory auction are inefficient. The relative revenue rankings of the auction formats can go in either direction, depending on the specifics of the environment. These conclusions regarding the efficiency and revenue ranking are in contrast to the previous literature, which focused on the case of independent information across agents.

Designing electricity auctions

Motivated by the new auction format in the England and Wales electricity market, as well as the recent debate in California, we characterize bidding behavior and market outcomes in uniform and discriminatory electricity auctions. Uniform auctions result in higher average prices than discriminatory auctions, but the ranking in terms of productive efficiency is ambiguous. The comparative effects of other market design features, such as the number of steps in suppliers' bid functions, the duration of bids, and the elasticity of demand are analyzed. We also consider the relationship between market structure and market performance in the two auction formats.

Auctions for government securities: A laboratory comparison of uniform, discriminatory and Spanish designs

The Bank of Spain uses a unique auction format to sell government bonds that can be seen as a hybrid of a uniform and a discriminatory auction. For winning bids above the average winning bid, buyers are charged the average winning bid; otherwise they pay their respective bids. We use experiments to compare this auction format to the discriminatory format used in most other countries and to the uniform format. Our design is based on a common value model with multi-unit supply and 2-unit demand. The Spanish and the uniform auctions raise significantly higher revenue than the discriminatory auction.

Sequential vs. Single-Round Uniform-Price Auctions

We study sequential and single-round uniform-price auctions with affiliated values. We derive symmetric equilibrium for the auction in which k1 objects are sold in the first round and k2 in the second round, with and without revelation of the first-round winning bids. We demonstrate that auctioning objects in sequence generates a lowballing effect that reduces first-round revenue. Thus, revenue is greater in a single-round, uniform auction for k = k1 + k2 objects than in a sequential uniform auction with no bid announcement. When the first-round winning bids are announced, we also identify two informational effects: a positive effect on second-round price and an ambiguous effect on first-round price. The expected first-round price can be greater or smaller than with no bid announcement, and greater or smaller than the expected price in a single-round uniform auction. As a result, total expected revenue in a sequential uniform auction with winning-bids announcement can be greater or smaller than in a single-round uniform auction.

Underpricing and Market Power in Uniform Price Auctions

In uniform auctions, buyers chosse demand schedules as strategies and the same market clearing price for units awarded. Despite the widespread use of these auctions, the extant theory shows that they are susceptible to arbitrarily large underpricing. We make a realistic modification to the theory by letting prices, quantities, and bids be discrete. We show that underpricing can be made arbitrarily small by choosing a sufficiently small price tick size and a sufficiently large quantitity multiple. We also show how one might improve revenues by modifying the allocation rule. A trivial change in the design can have a dramatic impact on prices. Our conclusions are robust to bidders being capacity constrained. Finally, we examine supply uncertainty robust equilibria.

Tacit Collusion in Repeated Auctions: Uniform Versus Discriminatory

Within an infinitely repeated game, I compare the level and conduct of collusion under uniform and discriminatory auctions. For this purpose, I characterize the optimal collusive schemes and sets of sustainable profits under these auction formats. I show that uniform auctions facilitate collusion more than discriminatory auctions: the optimal penal code is equally severe under the two formats; but bidders' deviation incentives are weaker in uniform auctions given that the pay‐off irrelevant bids can be used to relax the enforcement problem. This discussion is particularly relevant after the recent reforms in the electricity industry in England & Wales, and elsewhere.

Multiple Unit Auctions and Short Squeezes

This article develops a theory of multiunit auctions where short squeezes can occur in the secondary market. Both uniform and discriminatory auctions are studied and bidders can submit multiple bids. We show that bidders with short and long preauction positions have different valuations in an otherwise common value setting. Discriminatory auctions lead to more short squeezing and higher revenue than uniform auctions, ceteris paribus. Asymptotically, as the auction size approaches infinity, the two formats lead to equivalent outcomes. Shorts employ more aggressive equilibrium bidding strategies. Most longs strategically choose to be passive. Free riding on a squeeze by small, long players has no impact on these results, but affects revenue in discriminatory auctions. The problem of how to organize the sale of many identical units is often solved in practice by holding an auction where bidders can submit multiple bids for multiple units. Such auctions are important, not least because the auctioned assets often play prominent roles in the wider economy. Examples include auctions of treasury securities, electricity, gold, and money. The scale of these auctions and the frequency with which they are held add to their significance. An important feature of these auctions in practice is that bidders often have established forward positions in the underlying asset before the auction is actually held. Players that are short must cover their positions either by buying in the auction or in the postauction market. The risk of leaving it to the postauction market lies in the chance that a few bidders buy so much in the auction that they obtain market power in the secondary market. This power can be used to

Treasury auctions in Spain: a linear approach

Abstract. The majority of Treasuries use discriminatory auctions to sell government debt. A few Treasuries use uniform auctions. The Spanish Treasury is the only one that uses a hybrid format of discriminatory and uniform auctions. All Treasury auctions are multiple-unit multiple-bid auctions, usually assumed to be common and unknown value auctions. Taking in account these features, we analyze the Spanish auction format, taking a linear approximation to bidders' multiple bids, and characterize a parameter set in which the Spanish format gives higher expected seller's revenue than discriminatory and uniform auctions. Policy implications are obtained by calibrating theoretical results with data.

Do Uniform Price Auctions Trade‐off Higher Risk for Higher Return?*

AbstractResults of the recent US Treasury experiment comparing uniform and discriminatory price auctions suggest that uniform price auctions achieve lower award concentration and higher average revenues but experience higher variance of revenues from auction to auction relative to discriminatory price auctions. In other words, uniform pricing offers higher risk for higher return. This apparent trade‐off may deter some sellers considering the switch from discriminatory to uniform pricing; thus, it is important to investigate whether these results can be generalized. The Treasury's results are driven by the tendency for bidders in the uniform auctions to submit multiple bids at a wide range of prices, essentially steep bid curves, instead of the flat bids submitted in the discriminatory auctions. However, theory and data from discriminatory auctions in Sweden and Portugal suggest that bidders in discriminatory auctions will submit steeper bids when there is more potential for winner's curse. It is possible that bidders in the US auctions, which are preceded by a when‐issued market, are relatively unconcerned with the winner's curse. We examine the auction formats in an environment much more likely to generate the winner's curse: the initial public offering market. We compare discriminatory price auctions in Japan and uniform price auctions in Israel on the basis of revenue and slope of the demand curves and test a number of divisible good auction theory implications. In contrast with the Treasury's results, we find that revenues are likely to be insignificantly different in the discriminatory and uniform price auctions and that bid curves may be equally steep under both formats in markets with information asymmetry. The winner's curse increases underpricing and steepens demand curves in Japan's discriminatory price auctions but not in Israel's uniform price auctions.

Multiple Unit Auctions and Short Squeezes

This paper develops a theory of multiple unit auctions with short squeezes in the post-auction market. This is especially relevant for financial and commodity markets where players may enter the auction with established forward positions. We study how a potential short squeeze impacts on bidders' strategies and auction performance. Conversely, we also study how the design of the auction affects the incidence of short squeezes. In particular, we model both uniform price and discriminatory price auctions in a true multiple unit setting, where bidders can submit multiple bids for multiple units. Our model is cast in what appears to be a common value framework. However, we show that the possibility of a short squeeze introduces different valuations of the to-be-auctioned asset between short and long bidders. Equilibrium bidding strategies depend on pre-auction allocations and the size of the auction. Short squeezes are more likely to happen after discriminatory auctions than after uniform auctions, ceteris paribus. Discriminatory auctions therefore lead to (1) more price distortion; (2) higher revenue for an auctioneer; (3) more volatility in the secondary market. This shows that a central bank or sovereign treasury, say, may face a tradeoff between revenue maximization and market distortions when choosing the design of repo or treasury auctions. The probability of a short squeeze following a discriminatory auction tends to decrease with the auction size, increase with the market power of the largest long bidders, and decrease with small long players' scope for free-riding on a short squeeze. Asymptotically, as the auction size becomes arbitrarily large, the two types of auctions lead to equivalent outcomes.

Underpricing and Market Power in Uniform Price Auctions

In uniform auctions, buyers choose demand schedules as strategies and pay the same 'market clearing' price for units awarded. Despite the widespread use of these auctions, the extant theory shows that they are susceptible to arbitrarily large underpricing. We make a realistic modification to the theory by allowing discrete prices, quantities and bids. We show that underpricing can be made arbitrarily small by choosing a sufficiently small price tick size and a sufficiently large quantity multiple. We also show how one might improve revenues by modifying the allocation rule. A trivial change in the design can have a dramatic impact on prices. Our conclusions are robust to bidders being capacity constrained. Finally, we examine supply uncertainty robust equilibria.

Discriminatory versus uniform treasury auctions: Evidence from when-issued transactions

We use when-issued transactions data to assess the Treasury's current experiment with uniform auctions. When-issued volume is higher under uniform as compared to discriminatory auctions, suggesting a higher information release, which should reduce pre-auction uncertainty and the winner's curse. Under uniform auctions, when-issued volatility falls after the auction and again after the outcome announcement. The pattern is the opposite for discriminatory auctions. This is further evidence that uniform auctions increase pre-auction information and lower the short squeeze. A direct comparison of markups in uniform and discriminatory auctions yields mixed results.