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Price mechanism
Mechanism Design
For many centuries, auctions have been a common form of selling procedure. Although auction methods vary across country and product, the two most frequently observed are the open, ascending bid (or English) auction and the sealed-bid auction. Recent theoretical research has led to a theory of equilibrium bidding in these two auctions and a wide range of alternatives as well. As a result it has been possible to compare the revenue extracted by the seller under different auction methods and even to characterize the revenue-maximizing auction. The Revenue Equivalence Theorem (see for example, William Vickrey, 1961, Roger Myerson, 1981, and Riley and William Samuelson, 1981) asserts that when each bidder's reservation price for a unit of an indivisible good is an independent draw from the same distribution, and bidders are risk neutral, the sealed-bid auction generates the same expected revenue as the open auction. Much recent research has involved weakening each of the main hypotheses-risk neutrality, identically distributed values, and independence of values-in turn. We shall illustrate some of the principal conclusions of this work by considering the properties of open and sealed-bid auctions in a model of two bidders whose reservation prices can assume only two values, and by comparing these auctions to the optimal or revenuemaximizing auction. I. Revenue Equivalence
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We study a symmetric private value auction with signaling, in which the auction outcome is used by an outside observer to infer the bidders’ types. We elicit conditions under which an essentially unique D1 equilibrium bidding function exists in the second-price auction and the English auction. We establish there is no equivalence between these two auction designs, neither in bidding strategies nor in expected revenue. This is because the presence or absence of an increasing price clock, affects signaling incentives differently in both auction formats, and thereby also the bidders’ incentives to overbid their types. This leads to a strictly higher expected revenue in the second-price auction than in the English auction. Our analysis is completed by a comparison with other disclosure policies. Applications include art auctions and charity auctions.
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The auction mechanism has become an increasingly popular mechanism for price discovery where sellers seek to evaluate market interest. The winner's curse is a well established phenomenon associated with overbidding at auctions. However, auctioned properties could either be sold at the auction or through subsequent privately negotiated sales. Prior research indicates that the price from subsequent private sales could be higher than bids established at auctions. This study seeks to evaluate whether post-auction price movements differ with respect to at-auction or subsequent-to-auction transactions and with respect to non-auctioned sales. In so doing, we also seek to address the issue of winner's curse from a post-auction perspective.
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The auction mechanism has become an increasingly popular mechanism for price discovery where sellers seek to evaluate market interest. The winner's curse is a well established phenomenon associated with overbidding at auctions. However, auctioned properties could either be sold at the auction or through subsequent privately negotiated sales. Prior research indicates that the price from subsequent private sales could be higher than bids established at auctions. This study seeks to evaluate whether post-auction price movements differ with respect to at-auction or subsequent-to-auction transactions and with respect to non-auctioned sales. In so doing, we also seek to address the issue of winner's curse from a post-auction perspective.
English auction
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This dissertation consists of three essays covering applications of auction design. The first essay analyzes a model where a number of objects is sold in sequential second-price auctions. Each bidder has a privately known discount factor by which his valuation for an object decreases in each auction. The main result shows that prices decline in the sequence of auctions, even if corrected for the decrease in valuations. This result can explain the declining price anomaly and the afternoon effect. The second essay deals with impatience on the buyer's side and analyzes a Dutch auction, where the buyers' valuations decline while the auction runs. It turns out that the optimal behavior for the seller is either to run a very slow or a very fast auction. In a slow auction bidders do not find it profitable to wait and the auction is equivalent to a take-it-or-leave-it offer. In the fast auction the time preferences become less important and the auction becomes a sealed-bid-first-price auction. When comparing the expected revenue of the Dutch auction with that of a Japanese auction (with impatient buyers), the Japanese auction turns out to be better for the seller. The third essay analyzes a procurement auction where a firm plans to buy one of two different items. An auction format is described where the auction not only determines the price but also which item to procure. The auction is designed with practical applications in mind, i.e. it focuses on additive handicaps for bids the on less valued item.
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We study the optimal information disclosure policy in the optimal auction and the second-price auction when the seller has information that additively adjusts the independent private values of the bidders. In this setting, information revelation could change the allocation of the good in both types of auctions. However, in the optimal auction, the change in allocation makes the revenue function convex in the additive adjustments, so the seller should always reveal information. In contrast, in the second-price auction, the change in allocation makes the revenue function non-convex, in which case the seller might benefit from withholding information.
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Korean Abstract: 본 연구는 구조추정을 포함한 다양한 분석방법으로 온비드에서 진행된 승용차 공매자료를 분석하여 낙찰가에 영향을 주는 여러 요인과 그 특성을 파악하였다. 또한 분석 결과를 바탕으로 온비드에서 판매자수입을 극대화할 수 있는 공매방법에 대해 논의하였다. 온비드는 공공기관에 서 자산을 처분할 때 이용되고 있는 인터넷 입찰시스템이므로 온비드 입찰시스템의 최적 설계는 국내 자산처분시장의 효율성 제고에 중요하다. 주요한 분석 결과는 다음과 같다: (ⅰ) 온비드 승용차 공매에서 입찰자들의 정보구조는 독립적인 사적가치모형과 가장 부합한다; (ⅱ) 캠코 공매에서는 이용기관 공매보다 입찰자 수가 적고 감정평가금액 대비 낙찰가율이 낮았다; (ⅲ) 이 용기관 공매 중 2인 이상 유효한 입찰자가 있을 경우에만 유효한 입찰로 인정하는 공매에서는 입찰자 수가 적고 입찰자들의 사적가치가 낮았다; (ⅳ) 이용기관 공매에서 최저입찰가를 실제보다 5%, 10% 혹은 20% 올려 설정한 모의실험에서 판매자수입은 감소하였다. English Abstract: This paper analyzes Onbid car auction data by employing various methods, including structural estimation, to identify main factors which decides auction prices and figure out what effects those factors are making on the auction price. I then discuss on how to maximize sellers’ revenue in OnBid car auctions. The government and public institutes sell their assets through the OnBid auction, hence the optimal design of the OnBid auction is important. The paper’s main findings are as follows: (ⅰ) The independent private value model explains OnBid car auction data better than the correlated private value model or the interdependent value model; (ⅱ) Both the number of bidders and the ratios of the auction price to the evaluation value were lower in the auctions posted by the Kamco than auctions by institutes other than the Kamco; (ⅲ) Some auctions require that at least two bidders should submit a bid no less than the reserve price for sale. In those auctions, both the number of bidders and each bidder’s valuation on the auctioned object were lower than in auctions without that requirement; (ⅳ) The sum of sellers’ revenue would be decreased in the simulation with the reserve price higher by 5%, 10%, and 20% across auctions by institutes other than Kamco.
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The repeated nature of sponsored search auctions allows the seller to implement Myerson’s auction to maximize revenue using past data. But since these data are provided by strategic buyers in the auctions, they can be manipulated, which may hurt the seller’s revenue. We model this problem as a Private Data Manipulation (PDM) game: the seller first announces an auction (such as Myerson’s) whose allocation and payment rules depend on the value distributions of buyers; the buyers then submit fake value distributions to the seller to implement the auction. The seller’s expected revenue and the buyers’ expected utilities depend on the auction rule and the game played among the buyers in their choices of the submitted distributions. Under the PDM game, we show that Myerson’s auction is equivalent to the generalized first-price auction, and under further assumptions equivalent to the Vickrey–Clarke–Groves (VCG) auction and the generalized second-price auction. Our results partially explain why Myerson’s auction is not as popular as the generalized second-price auction in the practice of sponsored search auctions, and provide new perspectives into data-driven decision making in mechanism design.
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