Uniform Price Auction Research Articles

Allocating vehicle registration permits

We compare social welfare, consumer surplus and profits in two different institutional settings in which an item whose quantity is fixed and controlled (vehicle registration permit) is allocated to the buyers of a complementary good (car). In the first setting, which resembles the way in which vehicle registration permits are allocated in Singapore, the central planner runs a uniform price auction for permits in which the consumers who bid the highest receive the permits and pay the highest losing bid. Then each winning consumer purchases a car from a seller. In the alternative setting, the central planner first allocates the permits to sellers and then sellers offer to consumers bundles, each consisting of a car and a permit. For two different models of product differentiation, we find that social welfare is greater when permits are auctioned to consumers, but consumers and sellers generally prefer the alternative setting.

Equilibrium Selection in Hawk–Dove Games

We apply three equilibrium selection techniques to study which equilibrium is selected in a hawk–dove game with a multiplicity of equilibria. By using a uniform-price auction as an illustrative example, we find that when the demand in the auction is low or intermediate, the tracing procedure method of Harsanyi and Selten (1988) and the quantal response method of McKelvey and Palfrey (1998) select the same equilibrium. When the demand is high, the tracing procedure method does not select any equilibrium, but the quantal response method still selects the same equilibrium as when the demand is low or intermediate. The robustness to strategic uncertainty method of Andersson, Argenton and Weibull (2014) selects two of the multiple equilibria irrespective of the demand size. We also analyze the impact of an increase in the minimum bid allowed by the auctioneer in the equilibrium selection.

Optimal energy procurement with long-term photovoltaic energy contracts considering generation uncertainty: A two-dimensional auction approach

The procurement auction scheme for long-term photovoltaic (PV) energy contracts is being implemented in various countries to ensure stable profits for potential PV generators. However, in most of these auction formats, there is a deficiency in that they consider only the contract price and capacity, neglecting to account for the uncertainty of generation efficiency. In this regard, this study proposes a procurement auction scheme for long-term photovoltaic (PV) energy contracts based on mechanism design theory. We developed a two-dimensional auction model in which PV generators bid their cost and capacity. The energy buyer then determines the winners and enters into contracts with them for a fixed period. We incorporated the capacity factor into the payoff functions of both the buyer and the sellers to reflect different generation efficiencies of generators. Following the revelation principle, we characterized the incentive-compatible, individually rational direct mechanism that maximizes the buyer’s expected payoff during the contract period. We also proposed a computation algorithm to implement the auction. Numerical analysis using data from the Korean PV auction market suggested that the proposed model demonstrates results similar to the uniform price auction in terms of the levelized cost of electricity and contract price, and these results are lower than those of the Vickrey auction. Furthermore, despite the fact that the proposed auction results in a slight increase in social costs (approximately 1% more than the Vickrey auction), it maximizes the expected procured electricity and the auctioneer’s payoff.

Big Bids and Bidder Behavior in Uniform Price Auctions: Evidence from Peer-to-Peer Loan Markets

Big Bids and Bidder Behavior in Uniform Price Auctions: Evidence from Peer-to-Peer Loan Markets

Strategic supply management and mechanism choice in government debt auctions: An empirical analysis from the Philippines

We examine bond auctions in the Philippines by using bid data from around 500 Treasury auctions. The Philippines features a strategic auctioneer who uses both discriminatory and uniform-price auctions, and actively manages supply. Here, discriminatory auctions generate lower borrowing costs, at the expense of concentrating awards among fewer bidders. We observe that the decision to restrict supply is driven by borrowing cost and strength of demand. Bidders adjust for winner’ s curse by submitting bids with higher yield spreads in response to higher volatility and more competitors. Though bidder heterogeneity exists, average auction profits do not significantly differ across bidder types.

StableFees: A Predictable Fee Market for Cryptocurrencies

Blockchain-based cryptocurrencies must solve the problem of assigning priorities to competing transactions. The most widely used mechanism involves each transaction offering a fee to be paid once the transaction is processed, but this discriminatory price mechanism fails to yield stable equilibria with predictable prices. We propose an alternate fee setting mechanism, StableFees, that is based on uniform price auctions. We prove that our proposed protocol is free from manipulation by users and miners as the number of users and miners increases and show empirically that gains from manipulation are small in practice. We show that StableFees reduces the fees paid by users and reduces the variance of fee income to miners. Data from December 2017 show that, if implemented, StableFees could have saved Bitcoin users $272,528,000 USD in transaction fees while reducing the variance of miner’s fee income, on average, by a factor of 7.4. We argue that our fee protocol also has important social welfare and environmental benefits. This paper was accepted by Agostino Capponi, Special Section of Management Science: Blockchains and Crypto Economics. Supplemental Material: The data files are available at https://doi.org/10.1287/mnsc.2023.4735 .

Computational Performance of Deep Reinforcement Learning to Find Nash Equilibria

We test the performance of deep deterministic policy gradient—a deep reinforcement learning algorithm, able to handle continuous state and action spaces—to find Nash equilibria in a setting where firms compete in offer prices through a uniform price auction. These algorithms are typically considered “model-free” although a large set of parameters is utilized by the algorithm. These parameters may include learning rates, memory buffers, state space dimensioning, normalizations, or noise decay rates, and the purpose of this work is to systematically test the effect of these parameter configurations on convergence to the analytically derived Bertrand equilibrium. We find parameter choices that can reach convergence rates of up to 99%. We show that the algorithm also converges in more complex settings with multiple players and different cost structures. Its reliable convergence may make the method a useful tool to studying strategic behavior of firms even in more complex settings.

Bidding and Investment in Wholesale Electricity Markets: Discriminatory versus Uniform-Price Auctions Working Paper

Bidding and Investment in Wholesale Electricity Markets: Discriminatory versus Uniform-Price Auctions Working Paper

Selling Mechanism Design for Peer-to-Peer Lending and Related Markets: The Multi-Unit Uniform-Price Open Auction Versus Fixed Price

In the past two decades, there has been a decline in the use of uniform-price auctions in favor of fixed prices in markets of peer-to-peer lending, equity crowdfunding, and initial public offerings. This article aims to analytically study why this trend might be occurring. The analysis reveals that, relative to a fixed price, a uniform-price auction leads to more herding and strategic delay of bid submission and, consequently, a smaller transaction completion probability and lower expected revenue. These predictions are consistent with the empirical regularities observed for the bidding behavior and funding outcomes on Prosper, one of the leading peer-to-peer online lending platforms, and those documented in the literature for markets of equity crowdfunding and initial public offerings.

A motivational local trading framework with 2-round auctioning and settlement rules embedded in smart contracts for a small citizen energy community

We propose a motivational local trading framework with a 2-round auctioning system and a novel settlement approach to stimulate local transactions on the electricity surplus of a small community. Two auction price systems and several settlement mechanisms are formulated and compared to assess local trading profit and local market efficiency. We also implement a SC-based mechanism that embeds the auction results and rules to increase trust in the bidding and settlement processes. Our simulations use actual consumption and generation data from 11 houses with smart appliances and self-generation capabilities. We show that auctions, if used consistently, can help the development of a local trade by encouraging people to buy from their neighbors and invest in more generating facilities, knowing that there is a local market on which to rely. Compared to the hybrid - Pay-as-Bid (PaB) in the 1st round plus Uniform Price (UP) in the 2nd round - approach, the pure 2-round UP auction was shown to decrease trading with the retailer by 7.5%. The market indicators are quite similar for the two pricing methods, whereas the proposed settlement mechanism reduces the buyers' payments by 7% and increases sellers' encashments by around 8%.

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.

Auctioning business licenses to engage in Cournot competition

We study auctions for business licenses, where only the winners can participate in Cournot competition. This is an example of a multi-unit auction with endogenous and interdependent values. We compare a pay-as-bid auction and a uniform price auction. Assuming that only the winners’ identity and their payments are announced after the auction, the former auction is advantageous in terms of auction revenue, and the latter is advantageous in terms of consumer surplus.

An iterative uniform-price auction mechanism for peer-to-peer energy trading in a community microgrid

With the rapid deployment of distributed photovoltaic (PV) systems in residential buildings, peer-to-peer (P2P) energy trading in a community microgrid is highly desired since it enables flexible and economical energy transactions among neighboring prosumers. An efficient trading mechanism is pivotal for the successful and sustainable implementation of P2P energy trading in a community microgrid. This paper proposes a novel iterative uniform-price auction (IUPA) mechanism. Depending on the comparison between the aggregated energy supply and demand, the P2P market is divided into the seller’s market and the buyer’s market. The proposed auction mechanism is respectively implemented in the two types of markets in order to determine a uniform trading price and an efficient energy allocation. To maximize economic benefits, competitive prosumers iteratively adjust their bids based on their own private information and the issued market information until reaching a state of Nash equilibrium. This differs from the continuous double auction (CDA) in terms of bidding formats and prosumers’ trading strategies. Besides, the auction market self-adaption algorithm (AMSA) is designed for efficiently finding the equilibrium of the IUPA. Numerical studies demonstrate the effectiveness of the proposed mechanism in terms of finding fairer trading prices, saving total costs of the community, and promoting local transactions of excess PV energy.

Do Pay-As-Bid Auctions Favor Collusion? Evidence from Germany's market for reserve power

We analyze a drastic price increase in the German auction market for reserve power that did not appear to be driven by increased costs. Studying the market structure and bidding strategies using micro-level bidding data, we find a concentrated market with highly pivotal suppliers in an environment with completely inelastic demand and high entry barriers. We provide descriptive evidence that the price increase was triggered by an abuse of the “guess the clearing price” principle of discriminatory auctions via repeated pretended “bad guessing” of the marginal bid by the most dominant supplier. As intentional “bad guessing” of marginal bids is hard to prove, this suggests that the auction design is crucial for the competition authority's monitoring power – an issue that is often neglected in the discussion on the properties of auction designs. In fact, given regulatory threats, the deemed main advantage of pay-as-bid auctions over uniform price auctions and the popular belief that they reduce dominant suppliers' withholding incentives and diminish their ability to tacitly collude may be questioned in non-static settings. This suggests that pay-as-bid auctions may not necessarily reduce incentives for strategic capacity withholding and collusive behavior, but can even increase them when market power is high and demand inelastic, which is the case in virtually all energy markets.

Consignment auctions revisited

This paper studies the consignment auction as an allocation mechanism for emission permits among polluting firms. By assuming firms have non-increasing marginal values for the permits and linear bid functions, we characterize the linear equilibrium in a divisible consignment auction with positive trading volumes and a unique equilibrium price. We further compare the consignment auction with its uniform-price counterpart. We show that as firms acquire revenues from selling their consigned permits, they have incentives to overstate demands, which results in a higher equilibrium price in a consignment auction than in a uniform-price auction; nevertheless, the ex post efficiency ranking of these two auctions are generally ambiguous. Our results suggest that the non-trade equilibrium of Khezr and MacKenzie (2018) only appears when firms have a constant marginal value.

Consignment Auctions Revisited

This paper studies the consignment auction as an allocation mechanism for emission permits among polluting firms. By assuming firms have non-increasing marginal values for the permits and linear bid functions, we characterize the linear equilibrium in a divisible consignment auction with positive trading volumes and a unique equilibrium price. We further compare the consignment auction with its uniform-price counterpart. We show that as firms acquire revenues from selling their consigned permits, they have incentives to overstate demands, which results in a higher equilibrium price in a consignment auction than in a uniform-price auction; nevertheless, the ex post efficiency ranking of these two auctions are generally ambiguous. Our results suggest that the non-trade equilibrium of Khezr and MacKenzie (2018) only appears when firms have a constant marginal value.

Auction mechanisms for allocating subsidies for carbon emissions reduction: an experimental investigation

One method to reduce greenhouse gas emissions is to subsidize emissions-reducing activities, and allocating such subsidies through auctions is an emerging mechanism. In a controlled experimental market setting, we conduct a laboratory experiment to compare the effects of a variety of auction mechanisms for allocating subsidies in an effort to reduce carbon emissions in China. In addition to the conventional auction mechanisms, we place particular focus on testing the performance of the auction mechanism proposed by Erik Maskin (Notes on auctions for pollution reduction. In: Keynote Speech at the 18th annual conference of European Association for Environmental and Resource Economists, Rome, 2011). We find that while the Maskin auction mechanism spends the most from a fixed subsidy budget and its emissions reduction is among the largest, its per-unit emissions reduction cost is higher than that of discriminatory and uniform-price auction mechanisms. Furthermore, from the government’s perspective, the Maskin auctions exhibit strong improvement tendency with repeated auctions.

An allocatively efficient auction for pollution permits

This article proposes a new auction design for the efficient allocation of pollution permits. We show that if the auctioneer restricts the bidding rule of the uniform-price auction—coupled with a simple ex-post supply adjustment rule—then truthful bidding is obtained. Consequently, the uniform-price auction is more allocatively efficient than conventional formats that are currently observed in pollution markets.

Asymmetric Cost Pass‐Through in Multi‐Unit Procurement Auctions: An Experimental Approach*

We explore input cost pass‐through in multi‐unit procurement auctions. Whether cost shocks are private versus common across firms has important implications for discriminatory, but not uniform price auctions. We provide evidence of asymmetric pass‐through of private cost shocks in discriminatory auctions. Unlike uniform price auctions, revenue‐maximizing bidders in discriminatory auctions ‘pad’ bids close to the expected clearing price for units with costs below that price, but they do not bid below cost on higher cost units. Therefore, if costs are higher than expected, the clearing price rises and if costs are lower than expected, the clearing price remains high.

On the viability of energy-capacity markets under decreasing marginal costs

This study analyses markets for wholesale electricity that implement uniform-price auctions. We study a model with marginal cost-based regulatory pricing framework where the marginal cost of electricity generation is decreasing. The energy-capacity wholesale electricity market of Western Australia (WEM) is analysed for this purpose. Wholesale markets globally like the WEM need to remunerate electricity generators for the recovery of missing money in electricity generation to ensure resource adequacy as wholesale electricity prices further continue to decline. We show that marginal cost-based price regulation under decreasing marginal cost forces electricity generators to shut down as power producers cannot make a positive profit. The switch to average variable cost-based regulation also induces negative profit for electricity generators in some cases. We recommend that a market regulation under a uniform-price auction arrangement should include price caps to mitigate the high prices and volatility. In the long-term, the return to an energy-only market is a viable possibility. • We analyse markets for wholesale electricity that implement uniform-price auctions. • In our model the marginal cost of electricity generation is decreasing. • The energy-capacity wholesale electricity market of Western Australia (WEM) is analysed. • Marginal cost-based price regulation under decreasing marginal cost forces electricity generators to shut down. • Average variable cost-based regulation also induces negative profit for electricity generators in some cases.