Discriminatory Auction Research Articles

Market Design and Investment Incentives

The purpose of this study was to understand how market design affects market performance through its impact on investment incentives. For this purpose, we model capacity choices by two ex ante identical firms which compete in the product market. We analyse a number of different market design elements, including (i) two commonly used auction formats, the uniform‐price and discriminatory auctions, (ii) price caps and (iii) bid duration. We find that although the discriminatory auction tends to lower prices, this does not imply that investment incentives at the margin are poorer; indeed, aggregate capacity is the same under both auction formats.

Multi-unit auctions with private information: an indivisible unit continuous price model

We construct a model of multi-unit auctions in which I bidders bid for two indivisible units of a common value good. Using a first-order approach, we find that there are equilibria in which bidders bid the same price for both units in the discriminatory auction, but not in the uniform auction. When there are only two bidders, under certain conditions, there are linear equilibria for both the discriminatory and the uniform auction formats. In all equilibria, bidders equalize the expected marginal benefit of bidding to the marginal costs of bidding. We show that comparison of the seller’s expected revenue across auction formats depends only on the ratio of the precision of private information to the precision of public information.

Mechanism Choice and Strategic Bidding in Divisible Good Auctions: An Empirical Analysis of the Turkish Treasury Auction Market

We propose an estimation method to bound bidders’ marginal valuations in discriminatory auctions using individual bid-level data and apply the method to data from the Turkish Treasury auction market. Using estimated bounds on marginal values, we compute an upper bound on the inefficiency of realized allocations as well as bounds on how much additional revenue could have been realized in a counterfactual uniform price or Vickrey auction. We conclude that switching from a discriminatory auction to a uniform price or Vickrey auction would not significantly increase revenue. Moreover, such a switch would increase bidder expected surplus by at most 0.02 percent.

Supply function equilibria with capacity constraints and pivotal suppliers

The concept of a supply function equilibrium (SFE) has been widely used to model generators' bidding behavior and market power issues in wholesale electricity markets. Observers of electricity markets have noted how generation capacity constraints may contribute to market power of generation firms. If a generation firm's rivals are capacity constrained then the firm may be pivotal; that is, the firm could substantially raise the market price by unilaterally withholding output. However the SFE literature has not fully considered the impact of capacity constraints and pivotal firms on equilibrium predictions. We characterize the set of symmetric supply function equilibria for uniform-price auctions when firms are capacity constrained and show that this set is increasing as capacity per firm rises. We provide conditions under which asymmetric equilibria exist and characterize these equilibria. In addition, we compare results for uniform-price auctions to those for discriminatory auctions, and we compare our SFE predictions to equilibrium predictions of models in which bidders are constrained to bid on discrete units of output.

Price Dispersion in Electricity Auctions: The Strategic Foundation and Implication to Market Design

We model uniform and discriminatory auctions in wholesale electricity markets. High variability of electricity prices is often explained by exogenous economic factors. We, however, show that it can result endogenously from suppliers' strategic bidding, and that the connection between demand and price uncertainties is not direct, but manifested through bidders' assessments of capacity scarcity. Under symmetric and risk-neutral suppliers, the two auction formats yield the same expected procurement cost for buyers, but the discriminatory auction results in substantially lower price variance. When suppliers are risk-averse or have asymmetric capacities, expected procurement costs are also lower in discriminatory auctions.

Relative Performance Auctions

We study a multi-unit auction environment in which the bidding agents are rewarded according to the ranking of the surpluses that they make in the auction. We show that if a symmetric equilibrium exists in our auction game, then an efficient allocation may not be attainable. Our auction mechanism may be viewed as combining the features of both a discriminatory auction and a tournament. The inefficient outcome of our auction is remarkable because, when considered separately, both the the discrimininatory auction and the tournament yield efficient outcomes.

An Experimental Analysis of Auctioning Emission Allowances Under a Loose Cap

The direct sale of emission allowances by auction is an emerging characteristic of cap-and-trade programs. This study is motivated by the observation that all of the major implementations of cap-and-trade regulations for the control of air pollution have started with a generous allocation of allowances relative to recent emissions history, a situation we refer to as a “loose cap.” Typically more stringent reductions are achieved in subsequent years of a program. We use an experimental setting to investigate the effects of a loose cap environment on a variety of auction types. We find that all auction formats studied are efficient in allocating emission allowances, but auction revenues tend to be lower relative to competitive benchmarks when the cap is loose. Regardless of whether the cap is tight or loose, the different auction formats tend to yield comparable revenues toward the end of a series of auctions. However, aggressive bidding behavior in initial discriminatory auctions yields higher revenues than in the other auction formats, a difference that disappears as bidders learn to adjust their bids closer to the cut-off that separates winning and losing bids.

Auctions with variable supply: Uniform price versus discriminatory

We examine an auction in which the seller determines the supply after observing the bids. We compare the uniform price and the discriminatory auction in a setting of supply uncertainty, where uncertainty is caused by the interplay of two factors: the seller's private information about marginal cost and the seller's incentive to sell the profit-maximizing quantity, given the received bids. In every symmetric mixed strategy equilibrium, bidders submit higher bids in the uniform price auction than in the discriminatory auction. In the two-bidder case, this result extends to the set of rationalizable strategies. As a consequence, we find that the uniform price auction generates a higher expected revenue for the seller and a higher trade volume.

Uniform vs. discriminatory auctions with variable supply – experimental evidence

In the variable supply auction considered here, the seller decides how many customers with unit demand to serve after observing their bids. Bidders are uncertain about the seller's cost. We experimentally investigate whether a uniform or a discriminatory price auction is better for the seller in this setting. Exactly as predicted by theory, it turns out that the uniform price auction produces substantially higher bids, and consequently yields higher revenues and profits for the seller. Furthermore, again as predicted by theory, the uniform price auction yields a higher number of transactions, which makes it also the more efficient auction format.

Declining valuations and equilibrium bidding in central bank refinancing operations

Among the most puzzling observations on the euro money market are the discount in the weekly refinancing operations, the more aggressive bidding under uncertainty, the temporary flatness of bid schedules, and the development of interest rate spreads. To explain these observations, we consider a standard divisible-good auction with either uniform or discriminatory pricing, and place it in the context of a secondary market for interbank credit. The analysis links the empirical evidence to the endogenous choice of collateral in credit transactions. We also discuss the Eurosystem's preference for the discriminatory auction, the remuneration of reserves, and the impact of the recent market turmoil.

Revenues in discrete multi-unit, common value auctions: a study of three sealed-bid mechanisms

This paper proposes a discrete bidding model for both quantities and pricing. It has a two-unit demand environment where subjects bid for contracts with an unknown redemption value, common to all bidders. Prior to bidding, the bidders receive private signals of information on the (common) value. The relevant task is to compare the equilibrium strategies and the seller’s revenue of the three most common auction formats with two players. The result is that the Vickrey auction always gives the most revenue to the seller, the discriminatory auction follows closely and the uniform auction clearly is the worst due to demand reduction.

An Aproximation of the Optimality and Efficiency Problems of the Colombian Electricity Industry (Una Aproximación al Problema de Optimalidad y Eficiencia en el Sector Eléctrico Colombiano) (Spanish)

The paper proposes a theoretical model for understanding the functioning of the spot energy market in Colombia. In particular, it analysed the optimal performance for the three best-known types of multiunit auctions, Vickrey, discriminatory and uniform. The modelling, being a game of incomplete information includes features of the Colombian energy industry, such as reconciliations, private contracts and the uncertainty of the demand. The empirical analysis describes the sector in terms of efficiency and optimality. The efficiency’s literature referers to the condition in which winners of the auction are the agents with lower costs. Evidence of adverse effects have been found from the compensation mechanism for negative reconciliations in the perios of study (2000-2007). On the other hand, a mechanism is called optimal if it is the mechanism that leads to lower spending. The spending comparisons show that under a discriminatory auction could lead to a lower spending than the uniform one.

Sovereign debt auctions: Uniform or discriminatory?

Many financial assets, especially government bonds, are issued by an auction. An important feature of the design is the auction pricing mechanism: uniform versus discriminatory. Theoretical papers do not provide a definite answer regarding the dominance of one type of auction over the other. We investigate the revealed preferences of the issuers by surveying the sovereign issuers that conduct auctions. We find that the majority of the issuers/countries in our sample use a discriminatory auction mechanism for issuing government debt. We use a multinomial logit procedure and discriminatory analysis to investigate the mechanism choice. It was interesting to find that market-oriented economies and those that practice common law tend to use a uniform method while economies who are less market oriented and practice civil law tend to use discriminatory price auctions.

Demand Reduction and Preemptive Bidding in Multi-Unit License Auctions

Multi-unit ascending auctions allow for equilibria in which bidders strategically reduce their demand and split the market at low prices. At the same time, they allow for preemptive bidding by incumbent bidders in a coordinated attempt to exclude entrants from the market. We consider an environment where both demand reduction and preemptive bidding are supported as equilibrium phenomena of the ascending auction. In a series of experiments, we compare its performance to that of the discriminatory auction. Strategic demand reduction is quite prevalent in the ascending auction even when entry by the newcomer imposes a (large) negative externality on incumbents. As a result, the ascending auction performs worse than the discriminatory auction both in terms of revenue and efficiency, while the two auction formats offer similar chances for newcomers to enter the market.

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).

Discriminatory Versus Uniform-Price Electricity Auctions with Supply Function Equilibrium

The goal of this paper is to compare results for discriminatory auctions to results for uniform-price auctions when suppliers have capacity constraints. We have a pretty good understanding of what equilibrium results look like for the uniform-price auctions. But an unresolved problem is what happens when a discriminative auction is run and suppliers have capacity constraints. We formulate a supply function equilibrium model in continuous offer schedules with inelastic time-varying demand and with single-step marginal cost function to compare two auction institutions in the presence of capacity constraints. We show that payments made to the suppliers in the unique equilibrium of the discriminatory auction can be less than the payments in the uniform-price auction, depending on which uniform-price auction equilibrium is selected. For the high demand and/or low excess capacity cases, we characterize also mixed strategy supply function equilibrium under the discriminatory auction.

THE EFFECT OF AUCTION FORMAT ON EFFICIENCY AND REVENUE IN DIVISIBLE GOODS AUCTIONS: A TEST USING KOREAN TREASURY AUCTIONS*

This paper measures the efficiency and revenue properties of the two most popular formats for divisible goods auctions: the uniform‐price and discriminatory auction. We analyze bids into the Korean Treasury auctions which have used both formats. We find that the discriminatory auction yields statistically higher revenue. Unlike previous work that uses data from only one format, we are able to compare the efficiency properties of the two formats. We find that the discriminatory auction better allocates treasury bills to the highest value financial institutions. However, the differences in revenue and efficiency are not large because the auctions are very competitive.

Learning Agents in an Artificial Power Exchange: Tacit Collusion, Market Power and Efficiency of Two Double-auction Mechanisms

This paper investigates the relative efficiency of two double-auction mechanisms for power exchanges, using agent-based modeling. Two standard pricing rules are considered and compared (i.e., "discriminatory" and "uniform") and computational experiments, characterized by different inelastic demand level, explore oligopolistic competitions on both quantity and price between learning sellers/producers. Two reinforcement learning algorithms are considered as well--"Marimon and McGrattan" and "Q-learning"--in an attempt to simulate different behavioral types. In particular, greedy sellers (optimizing their instantaneous rewards on a tick-by-tick basis) and inter-temporal optimizing sellers are simulated. Results are interpreted relative to game-theoretical solutions and performance metrics. Nash equilibria in pure strategies and sellers' joint profit maximization are employed to analyze the convergence behavior of the learning algorithms. Furthermore, the difference between payments to suppliers and total generation costs are estimated so as to measure the degree of market inefficiency. Results point out that collusive behaviors are penalized by the discriminatory auction mechanism in low demand scenarios, whereas in a high demand scenario the difference appears to be negligible.

Auctions with Variable Supply: Uniform Price Versus Discriminatory

We examine an auction in which the seller determines the supply after observing the bids. We compare the uniform price and the discriminatory auction in a setting of supply uncertainty. Uncertainty is caused by the interplay of two factors: the seller's private information about marginal cost, and the seller's incentive to sell the profit-maximizing quantity given the received bids. In every symmetric mixed strategy equilibrium, bidders submit higher bids in the uniform price auction than in the discriminatory auction. In the two-bidder case this result extends to the set of rationalizable strategies. As a consequence, we find that the uniform price auction generates higher expected revenue for the seller and higher trade volume

Discriminatory Versus Uniform-Price Electricity Auctions with Supply Function Equilibrium

A goal of this paper is to compare results for discriminatory auctions to results for uniform-price auctions when suppliers have capacity constraints. We have a pretty good understanding of what equilibrium results look like for the uniform-price auctions. But an unresolved problem is what happens when a discriminative auction is run and suppliers have capacity constraints. We formulate a supply function equilibrium (SFE) model in continuous offer schedules with inelastic, time varying demand and with single step marginal cost function to compare two auction institutions in the presence of capacity constraints. We show that payments made to the suppliers in the unique equilibrium of the discriminatory auction can be less than the payments in the uniform-price auction, depending on which uniform-price auction equilibrium is selected. For the high demand and/or low excess capacity cases we also characterize mixed strategy supply function equilibrium under the discriminatory auction.