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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)

We reexamine the characterization of incentive compatible single-parameter mechanisms introduced in Archer & Tardos(2001). We argue that the claimed uniqueness result, called `Myerson's Lemma' was not well established. We provide an elementary proof of uniqueness that unifies the presentation for two classes of allocation functions used in the literature and show that the general case is a consequence of a little known result from the theory of real functions. We also clarify that our proof of uniqueness is more elementary than the previous one. Finally, by generalizing our characterization result to more dimensions, we provide alternative proofs of revenue equivalence results for multiunit auctions and combinatorial auctions., 17 pages

We consider a digital product seller who needs to determine the number of items to sell and its price over an infinite horizon. The seller indeed owns unlimited supply of the digital products like music or software. Each buyer is risk-neutral and needs one unit of the product. The number of buyers in each period and their private valuations are random. The seller conducts an auction to allocate the items in each period. The buyers who fail to gain one item in the previous periods will rebid in the subsequent auctions. Regarding the formulated dynamic program, we prove that the optimal allocation solution is a variant of the base-stock policy. Based on the known Revenue Equivalence Principle, we also prove that the generalized second-price auction and the first-price auction will result in the same expected revenue for the seller. Finally, with mild technical modifications, the results of the infinite-horizon case can be extended to the finite-horizon case even if the demand is time-varying stochastic and independent.

We study information aggregation when n bidders choose, based on their private information, between two concurrent common-value auctions. There are k(s) identical objects on sale through a uniform-price auction in market s and there are an additional k(r) objects on auction in market r, which is identical to market s except for a positive reserve price. The reserve price in market r implies that information is not aggregated in this market. Moreover, if the object-to-bidder ratio in market s exceeds a certain cutoff, then information is not aggregated in market s either. Conversely, if the object-to-bidder ratio is less than this cutoff, then information is aggregated in market s as the market grows arbitrarily large. Our results demonstrate how frictions in one market can disrupt information aggregation in a linked, frictionless market because of the pattern of market selection by imperfectly informed bidders., European Research Council (ERC)

We study implementability and revenue equivalence for selling mechanisms in a model where a seller has multiple items to allocate, and a buyer has private valuations and private budgets. We provide necessary and sufficient conditions for selling mechanisms to be incentive compatible and ex-post budget feasible for the buyer and derive the revenue equivalence principle in the presence of private budgets. Our conditions are based on a novel network approach that exploits the difference between unrestricted incremental values —the minimal value difference between an item assigned to the buyer by the seller and another alternative— and restricted incremental values —the minimal value difference between the assigned item and the alternative when the buyer can actually afford the alternative, given her financial disposition. We derive properties of incentive compatible, budget feasible prices, and illustrate our approach in a multi-item allocation problem with a convex type space.

We analyze the role of auctions in managing the default of a central counterparty's clearing member. We first consider two established sealed-bid auction formats in which clearing members simultaneously submit bids for a defaulting clearing member's portfolio: first price and first price with budget constraints. We argue that the use of some form of penalty could have significant implications for financial stability by inefficiently distributing losses deriving from the unallocated portfolio to surviving clearing members. In response to these potential adverse implications, we propose a third auction type, second price with loss-sharing, which increases the revenue by allowing bidders to consider potential losses within their bidding function without passively waiting for a possible form of penalty.

In a field experiment, we study the revenue-generating properties of premium auctions. In a premium auction, the runner-up obtains a premium for driving up the price paid by the winner. Previous research, both theoretical and in the lab, has shown that the relative performance of premium auctions compared to standard auction formats is context-specific. In the experiment, we compare two types of premium auctions with the standard Vickrey auction selling high-quality, limited-edition posters in an online auction. We observe that neither premium auction raises higher revenue than the Vickrey auction. Revenue dispersion in the Amsterdam auction, one of the premium auctions, is lower than that in the other two auctions.

We characterize revenue maximizing mechanisms in a common value environment where the value of the object is equal to the highest of bidders’ independent signals. If the object is optimally sold with probability one, then the optimal mechanism is simply a posted price, with the highest price such that every type of every bidder is willing to buy the object. A sufficient condition for the posted price to be optimal among all mechanisms is that there is at least one potential bidder who is omitted from the auction. If the object is optimally sold with probability less than one, then optimal mechanisms skew the allocation towards bidders with lower signals. This can be implemented via a modified Vickrey auction, where there is a random reserve price for just the high bidder. The resulting allocation induces a “winner's blessing,” whereby the expected value conditional on winning is higher than the unconditional expectation. By contrast, standard auctions that allocate to the bidder with the highest signal (e.g., the first-price, second-price or English auctions) deliver lower revenue because of the winner's curse generated by the allocation rule. Our qualitative results extend to more general common value environments where the winner's curse is large.

I introduce an empirical auction model where in addition to the private value that each bidder receives upon winning the auction, losing bidders incur a negative externality that depends on the identity of the rival winner. I show how the externalities and private value distributions can be identified and estimated in such a model. I then apply the model to U.S. Forest Service timber auctions. I find that mill bidders impose significant externalities on one another of between 10% and 22% of the heterogeneous portion of their valuation. This leads the timber tracts to be misallocated in 5.2% of the auctions in my sample.

Auctions for allocating resources and determining prices have become widely applied for services over the Internet, Cloud Computing, and Internet of Things in recent years. Very often, such auctions are conducted multiple times. They may be expected to gradually reveal participants’ true value distributions, with which, it eventually would result in a possibility to fully apply the celebrated Myerson's optimal auction to extract the maximum revenue, in comparison to all truthful protocols. There is however a subtlety in the above reasoning as we are facing a problem of exploration and exploitation, i.e., a task of learning the distribution and a task of applying the learned knowledge to revenue maximization. In this work, we make the first step effort to understand what economic settings would make this double task possible exactly or approximately. The question opens up greater challenges in the wider areas where auctions are conducted repeatedly with a possibility of improved revenue in the dynamic process, most interestingly in auctioning cloud resources.

Purpose The purpose of this paper is to design a parking space management platform to alleviate the parking problem and a two-stage solution for sharing and allocating parking spaces. Design/methodology/approach The market design mechanism and auction mechanism are integrated to solve the problem of parking space sharing and allocation. In the first stage, the market design mechanism with two rules is applied for making the good use of idle parking spaces. In the second stage, two sequential auction mechanisms are designed by extending first/second-price sealed bid auction mechanism to allocate both private and public parking spaces, which are received in previous stage and owned by the platform. Two stages are connected through a forecasted price which is calculated through the exponential smoothing method. Findings First, we prove three important properties of the proposed sequential auction mechanisms, namely, incentive compatibility, revenue equivalence and individual rationality. Second, a simulation study is used to verify the effectiveness of the mechanisms through numerical analysis. The impact of the system on three parts, namely, agents (private parking space suppliers), bidders (parking space customers) and the platform, is examined. Third, the results show that the sharing mechanism with monetrary incentive will attract a number of agents to join in the platform. The bidders are also able to obtain considerable utility, as compared with the (average) market parking fees. The platform can thus effectively allocate parking spaces with reasonable prices. Originality/value This paper combines the classical sequential auction mechanisms with the market design mechanism for the parking space sharing and allocation problem. The modeling and analysis method can also be used to address the similar allocation and pricing problems of other resources like bicycle sharing.

Purpose In this paper, the main focus is on supply and demand auction systems with resource pooling in modern supply chain from a theoretical modeling perspective. The supply and demand auction systems in modern supply chains among manufacturers and suppliers serve as information sharing mechanisms. The purpose of this paper is to match the supply and demand such that a modern supply chain can achieve incentive compatibility and economic efficiency. The authors design such a supply and demand auction system that can integrate resources to efficiently match the supply and demand. Design/methodology/approach The authors propose three theoretic models of modern supply chain auctions with resource pooling according to the Vickrey auction principle. They are supply auction model with demand resource pooling, demand auction model with supply resource pooling, and double auction model with demand and supply resource pooling. For the proposed auction models, the authors present three corresponding algorithms to allocate resources in the auction process by linear programming, and study the incentive compatibility and define the Walrasian equilibriums for the proposed auction models. The authors show that the solutions of the proposed algorithms are Walrasian equilibriums. Findings By introducing the auction mechanism, the authors aim to realize the following three functions. First is price mining: auction is an open mechanism with multiple participants. Everyone has his own utility and purchasing ability. So, the final price reflects the market value of the auction. Second is dynamic modern supply chain construction: through auction, firm can find appropriate partner efficiently. Third is resources integration: in business practices, especially in modern supply chain auctions, auctioneers can integrate resources and ally buyers or sellers to gain more efficiency in auctions. Originality/value In the paper, the authors propose three theoretic models and corresponding algorithms of modern supply chain auctions with resource pooling according using the Vickrey auction principle, which achieves three functions: price mining, dynamic modern supply chain construction and resources integrating. Besides, these proposed models are much closer to practical settings and may have potential applications in modern supply chain management.

We revisit the revenue comparison of standard auction formats, including first-price, second-price, and English auctions. We rank auctions according to their revenue guarantees, i.e., the greatest lower bound of revenue across all informational environments, where we hold fixed the distribution of bidders’ values. We conclude that if we restrict attention to the symmetric affiliated models of Milgrom and Weber (1982) and monotonic pure-strategy equilibria, first-price, second-price, and English auctions are revenue guarantee equivalent: they have the same revenue guarantee, which is equal to that of the first-price auction as characterized by Bergemann, Brooks, and Morris (2017). If we consider all equilibria or if we allow more general models of information, then first-price auctions have a greater revenue guarantee than all other auctions considered. (JEL D44, D83)

Received auction theory prescribes that a reserve price which maximizes expected profit should be no less than the seller's own value for the auctioned object. In contrast, a common empirical observation is that many auctions have reserve prices set below sellers' values, even at zero. This paper revisits the theory to find a potential resolution of the puzzle for second-price auctions. The main result is that an optimal reserve price may be less than the seller's value if bidders are risk averse and have interdependent values. Moreover, the resulting outcome may be arbitrarily close to that of an auction that has no reserve price, an absolute auction.

In many cases, agents that make purchase decisions are uninformed and rely on the advice of biased experts. For example, when contemplating an acquisition, the board of the bidder relies on the advice of the managerial team when deciding what oer to make for the target. In this paper, we study how to sell assets to such \advised buyers" if the goal is (i) to maximize revenues; (ii) to maximize allocative eciency. In static mechanisms, such as rst- and second-price auctions, advisors communicate a coarsening of information and a version of the revenue equivalence theorem holds. In contrast, dynamic mechanisms, such as multiple-round auctions, result in more informative communication between buyers and their advisors, which leads to more ecient allocations and may lead to higher revenues. When advisors are biased toward overpaying, an ascending-price auction dominates any static mechanism in terms of both eciency and revenues. When advisors are biased towards underpaying, a descendingprice auction dominates static mechanisms in terms of eciency but often results in

We study the role of limited commitment in a standard auction environment. In each period, the seller can commit to an auction with a reserve price but not to future reserve prices. We characterize the set of equilibrium profits attainable for the seller as the period length vanishes. An immediate sale by efficient auction is optimal when there are at least three buyers. For many natural distributions two buyers is enough. Otherwise, we give conditions under which the maximal profit is attained through continuously declining reserve prices. (JEL D44, D82)

Project procurement has two important attributes: cost uncertainty and failure risk. Due to the incomplete feature of such attributes, a novel mechanism incorporating contingent payments and cost sharing contracts is proposed for the buyer. Constructing models of bid decisions for risk averse and risk neutral suppliers, respectively, closed-form solutions of optimal bid prices are derived. By investigating the properties of bid prices in a first-score sealed-bid reverse auction, we find that when the degree of risk aversion or the variance of unpredictable cost is sufficiently small, bid prices of risk averse suppliers could be lower than those of risk neutral suppliers. Yet risk averse suppliers always bid higher than risk neutral suppliers in a second-score sealed-bid reverse auction. An interesting result verified by numerical experiments is that the classical revenue equivalence theorem no longer holds for the proposed mechanism if suppliers involve risk averse behavior. In this case, the buyer's best choice is to adopt a first-score sealed-bid reverse auction. We also provide decision support for the buyer to achieve optimal expected profit.

In this chapter, we evaluate the seller’s expected revenue in different auction formats and show under which contexts this revenue is equivalent. First, Exercise 6.1 considers the first-price, second-price, third-price, and all-pay auctions from the previous chapters, evaluating the expected revenue that each of them generate, and showing that the expected revenue coincides.

This chapter is an introduction to game theory, and to its application to situations of asymmetric information. It covers simultaneous and sequential games, dominant strategies, Nash equilibrium, backward induction, subgame perfection, repeated games, Bayesian games, sequential rationality, behavioural strategies, perfect Bayesian equilibrium, sequential equilibrium. The Centipede game is taken as an incentive to be critical of the usual definition of rationality; some doubts are also raised about the universal certainty that dominant strategies will always be played: some examples of Prisoners’ Dilemma suggest as plausible that players may choose ‘Cooperate’. The treatment of auctions is limited but rigorous, it is proved that a first-price sealed-bid (independent-private-values) auction and a second-price sealed-bid auction generate the same expected revenue for the seller, and on this basis the revenue equivalence theorem is sketched; for common-value auctions the winner’s curse is examined in detail. Then the chapter passes to asymmetric information, and discusses principal-agent, moral hazard, adverse selection, screening, signalling, and the intuitive criterion of Cho and Kreps. The dependence of all these analyses on the assumption that agents choose on the basis of VNM expected utility, which does not seem to correspond to how people actually choose, is noticed.

I study sequential first-price auctions where two items are sold to two bidders with private binary valuations. A seller, prior to the second auction, can publicly disclose some information about the outcome of the first auction. I characterize equilibrium strategies for various disclosure rules when the valuations of bidders are either perfectly positively or perfectly negatively correlated across items. I establish outcome equivalence between different disclosure rules. I find that it is optimal for the seller to disclose some information when the valuations are negatively correlated, whereas it is optimal not to disclose any information when the valuations are positively correlated. For most of the parameter values, the seller’s expected revenue is higher if the losing bid is disclosed. When only the winner’s identity is disclosed, the equilibrium is efficient whether the valuations are positively or negatively correlated.

The authors study optimal auctions in a symmetric private values setting, where bidders’ care about winning the object and a receiver’s inference about their type. They reestablish revenue equivalence when bidders’ signaling concerns are linear, and the auction makes participation observable via an entry fee. With convex signaling concerns, optimal auctions are fully transparent: every standard auction, which reveals all bids yields maximal revenue. With concave signaling concerns there is no general revenue ranking. The authors highlight a trade-off between maximizing revenue derived from signaling, and extracting information from bidders. Their methodology combines tools from mechanism design with tools from Bayesian persuasion.

We study uniform-price double auctions augmented with a class of subsidy schemes. Using these subsidies, any profile of linear demand schedules can be implemented as an equilibrium outcome. By revenue equivalence, all other mechanisms which implement linear auction equilibria are essentially equivalent to some subsidy scheme in our class. We show that, under a linear dependency condition on primitives, fully efficient, budget balanced, and individually rational trade is possible. Thus, the welfare loss from equilibria in uniform-price auctions without subsidies is a non-fundamental distortion, which can be fixed with better mechanism design. However, we show that monopolist trading platforms have incentives to reduce allocative efficiency to increase revenue, even as the number of traders becomes large.

The authors study optimal auctions in a symmetric private values setting, where bidders’ care about winning the object and a receiver’s inference about their type. They reestablish revenue equivalence when bidders’ signaling concerns are linear, and the auction makes participation observable via an entry fee. With convex signaling concerns, optimal auctions are fully transparent: every standard auction, which reveals all bids yields maximal revenue. With concave signaling concerns there is no general revenue ranking. The authors highlight a trade-off between maximizing revenue derived from signaling, and extracting information from bidders. Their methodology combines tools from mechanism design with tools from Bayesian persuasion.

The pay-as-bid auction is a prominent format for selling homogenous goods such as treasury securities and commodities. We analyze the optimal design of pay-as-bid auctions allowing for asymmetric information. We show that supply transparency and full disclosure are optimal in pay-as-bid, though not necessarily in uniform-price (the main alternative auction format). Pay-as-bid is revenue dominant and might be welfare dominant. Under assumptions commonly imposed in empirical work, the two formats are revenue and welfare equivalent.

This chapter is dedicated to Goethe’s price game which can be interpreted as a second-price sealed-bid auction. Nobel Laureate William Vickrey has shown for this type of auction that bidding one’s willingness-to-pay price is an optimal strategy. We do not know whether Goethe had a similar result in mind. In fact, his sealed-bid price functioned like a take-it-or-leave-it option. Given the historical circumstances, it implied price-fixing, thereby avoiding explicit bargaining. A discussion of the Revenue Equivalence Theorem adds some theory to Goethe’s auction setting. The theorem says that, in principle, first-price sealed-bid auctions, Dutch auctions, second-price sealed-bid auctions, and English auctions pick the same winners and have identical prices. There are other types of auctions as well, and some have rather peculiar effects. All-pay auctions are recommended for exploiting bidders—as in collecting money for a charity. If you want to win, do not participate. English auctions can have peculiar results, too. You might be interested in paying a high auction price for Gauguin’s “Mata Mua” if you already have a number of Gauguin paintings in your collection. On May 9, 1989, the “Mata Mua” was auctioned by Sotheby at 24.2 million dollars, then being the highest price ever bid for a Gauguin painting. You might also be willing and able to pay a high auction price if you represent a consortium of the Federal Republic of Germany, the States of Lower Saxony and Bavaria, the Prussian Cultural Heritage Foundation, and private donators. On December 6, 1983, the gospel book of Henry the Lion (1129–1195) was auctioned and sold for a price of £8,140,000, then equaling 32.5 million German marks. There was a single bidder present in the auction hall, i.e., the representative of the consortium, and a second person calling bids from outside—possibly the seller.

A marketable permit system (MPS) has been suggested as a solution to environmental problems. Although the properties of MPSs under non-trader settings, in which each player is exclusively either a seller or a buyer, are well documented, little research has explored how MPSs perform under trader settings, in which each player can be both a seller and a buyer. We institute two auctions of trader settings in MPS experiments: a double auction (DA) and a uniform price auction (UPA). We then evaluate and compare their performances both with each other and with those under non-trader settings. The main results are as follows: DAs under trader settings perform much worse than do DAs under non-trader settings, whereas UPAs perform well, regardless of the trader and non-trader settings. UPAs are more efficient and generate more stable prices than do DAs under trader settings, and a considerable proportion of trades in DAs under trader settings consist of “flips” that could be considered speculation or errors. Thus, UPAs are likely to work better than DAs under trader settings.

The standard revenue-maximizing auction discriminates against a priori stronger bidders so as to reduce their information rents. We show that such discrimination is no longer optimal when the auction’s winner may resell to another bidder, and the auctioneer has non-Bayesian uncertainty about such resale opportunities. We identify a “worst-case” resale scenario, in which bidders’ values become publicly known after the auction and losing bidders compete Bertrand-style to buy the object from the winner. With this form of resale, misallocation no longer reduces the information rents of the high-value bidder, as he could still secure the same rents by buying the object in resale. Under regularity assumptions, we show that revenue is maximized by a version of the Vickrey auction with bidder-specific reserve prices, first proposed by Ausubel and Cramton (2004). The proof of optimality involves constructing Lagrange multipliers on a double continuum of binding non-local incentive constraints.

I study revenue maximizing mechanisms in the presence of agents who are loss averse in the sense of Koszegi and Rabin (Quart J Econ 121:1133–1166, 2006, Am Econ Rev 97:1047–1073, 2007). Since the reference point is formed endogenously as an equilibrium object, the principal can influence the agents’ reference points by announcing a particular mechanism. Two specifications of reference-dependence are considered. If the agents narrowly bracket gains and losses in the good and in the money dimension separately, any optimal mechanism is all pay, and an optimal auction is an all pay auction with minimum bid; with wide bracketing of gains and losses over the entire risk neutral payoff, an optimal auction is a first price auction with minimum bid. Compared to the same environment with risk neutral agents, the minimum bid is always weakly higher with narrow bracketing and always weakly lower with wide bracketing of gains and losses. In case loss aversion is very pronounced, differentiability of the value function fails, and no familiar characterization of incentive compatibility involving the envelope theorem is available.

With an effort to allocate divisible resources among suppliers and consumers, a double-sided auction model is designed to decide strategies for individual players. Under the auction mechanism with the Vickrey–Clarke–Groves-type payment, the incentive compatibility holds, and the efficient bid profile is a Nash equilibrium (NE). However, it brings difficulties for players to implement the efficient solution due to the fact that there exist infinite number of NEs in the underlying double-sided auction game. To overcome this challenge, we formulate the double-sided auction game as a pair of single-sided auction games which are coupled via a joint potential quantity of the resource. A decentralized iteration procedure is then designed to achieve the efficient solution, where a single player, a buyer, or a seller implements his best strategy with respect to a given potential quantity and a constraint on his bid strategy. Accordingly, the potential quantity is updated with respect to iteration steps as well. It is verified that the system converges to the efficient NE within finite iteration steps in the order of $\mathcal {O}(\ln (1/\varepsilon))$ with $\varepsilon$ representing the termination criterion of the algorithm.