Multi-Unit Auctions: A Literature Rewiev

Also it would be reasonable to distinguish auctions by bidderswho demand just one unit of the good, which is called singletondemand, or bidders who demand more than one unit of good.Milgrom(2004) describe multi unit auctions as more complex than thesingleton demand auction. It is more complex because first thenumber of different allocations increases exponentially. For a singleobject and five bidder case there is only five possible allocation whilefor a five unit and five bidders case it would be 5 5 =3125 differentallocations. Secondly, singleton demand eliminate the tension ofefficiency problem, while for multi-unit auctions it is a little bitcumbersome. For example, Vickrey auction can improve the efficiencyproperties of a singleton demand auction, but it can bring about zeroprofit or lower profit for the multi unit auctions. Thirdly, there is aproblem of so-called value discovery. With singleton demand there isonly one object to value, on the contrary, in the multi unit auction, theexponentially larger number of different allocation can force a bidderto reduce his valuation. Hence, Vicrey auction can cause severeefficiency problems in multi-unit auctions.Researches in this area contributed economic theory varioustype of issues and analysis tools that are absent in the single-objectauction literature. Ausubel(2004) suggested a new dynamic auctionformat. Also, Generelized Vickrey Auction or Vickrey-Groves-Clarkemechanism has been introduced to economic theory.In section II, I specified some terminology and classification ofmulti unit auctions. Theoretical concepts of the multi-unit auction fromliterature are presented. In section III, I give some examples of

pays the same price. This price is typically the highest price among thelooser bids. It looks like the second price auction. Second,Discriminatory Price Rule: Each winner pays what he bids for and theunit that he won. It is also called pay-as bid or pay your bid auctions.It is similar to the case of monopolist imposing discriminatory pricing.Donald et al.(2006) tell about a pricing rule which can be stated todetermine a price such that all available units are sold. This is a specialcase of uniform price.It was believed that bidders will shade their bids underdiscriminatory pricing rule. in the single object context, a bidder willnot reveal his true valuation if he is going to pay what he had bided.Some people argued that under uniform pricing rule people may valueclose to their true valuation.Revenue comparison between these two regimes is vague.Friedman proposed that uniform pricing will bring more revenue forthe sale of treasury bills, therefore US Treasury bills had been soldaccording to uniform pricing rule. Ausuman and Cramton(1998)showed that even under uniform pricing rule bidders have incentive toshade their bids. This is called demand reduction. They described thatan ideal mechanism would be the one that price and bid are notrelated.Ausubel and Crampto(1998) try to explain and challenge thecommon belief of so-called the uniform-price auction fallacy.Academics and policymakers have observed that the pay-your-bidauction can be viewed as a multi-unit extension of the first-priceauction, and have asserted that the uniform-price auction is best

egarded as a multi-unit extension of the second price auction. Theydemonstrate, under general circumstances, that a bidder who desiresmore than one unit in a uniform-price auction has an incentive toshade his bid. In another words they prove an Inefficiency Theoremwhich establishes that every equilibrium of the uniform-price auction isex post inefficient with positive probability. They showed that in somefairly reasonable situations where efficiency was impossible in auniform-price auction, full efficiency is, nevertheless, possible in a payyour-bidauction.We know that the auctions literature has provided us with twofundamental prescriptions guiding effective auction design. First, anauction should be structured so that the price paid by a playerconditional on winning-is independent of her own bids. Ideally, thewinner's price should depend solely on opposing participants' bids-asin the sealed-bid, second-price auction-so that each participant has fullincentive to reveal truthfully his valuation for the good. Second, anauction should be structured in an open fashion that maximizes theinformation made available to each participant at the time she placesher bids. This result is due to Milgrom and Weber’s celebrated 1982apaper.Ausubel(2004) propose a new ascending–bid auction which iscalled Ausubel Auction. The auctioneer announces a price and biddersrespond with quantities. Items are awarded at the current pricewhenever they are “clinched,” and the price is incremented until themarket clears. Ausubel showed that with private values, this (dynamic)auction yields the same outcome as the (sealed-bid) Vickrey auction,

ut has advantages of simplicity and privacy preservation and withinterdependent values, this auction may retain efficiency.Bid Shading, Demand ReductionBid shading describes the practice of a bidder placing a bid thatis below what they believe a good is worth.Bid shading is used for one of two purposes. In a common valueauction with incomplete information, bid shading is used tocompensate for the winner's curse. In such auctions, the good is worththe same amount to all bidders, but bidders don't know the value ofthe good and must independently estimate it. Since all bidders valuethe good equally, the winner will generally be the bidder whoseestimate of the value is the largest. But if we assume that in generalbidders estimate the value accurately, then the highest bidder hasoverestimated the good's value and will end up paying more than itworths. In other words, winning the auction carries bad news about abidder's value estimate. A savvy bidder will anticipate this, and reducehis bid accordingly.Bid shading is also used in first-price auctions, where the winningbidder pays the amount of his bid. If a participant bids an amountequal to their value for the good, they would gain nothing by winningthe auction, since they are indifferent between the money and thegood. Bidders will optimize their expected value by accepting a lowerchance of winning in return for a higher payoff if they win. manypeople believed that uniform pricing, which is analogous to secondprice auction, would have all good properties of Vicrey auction namelyit would be truth-telling and efficient. However, Ausubel and

Generalize Vickrey Auctions.Generalized Vickrey Acution (GVA) or Vickrey –Groves –Clarke isanalysed as an analogous mechanism of Vickrey auctions for multiunit auctions. For GVA, all units for sale are allocated to the bidderswho have the highest reported valuations, but the price each winnerpays does not depend on his report but rather on the bids of theothers.Ausubel AuctionAusubel(2004) conjectured that an auction should posses twoquality to be efficient. First, the price a bidder pays should beindependent of his actions, bids. Second, an auction should bestructured so as to maximize the amount of information available toparticipants.The Generalized Vickrey Acution (GVA) satisfy the firstrequirement, but since it is a sealed- bid auction it does not disclosethe information. Ausubel proposed a new auction to satisfy the secondrequirement. According to this auction rules, the auctioneer calls aprice, bidders respond with quantities.This process iterates until thedemand is equal to supply A bidder do not pay the market clearingprice.but the auctioneer decide at each price the aggregate demandfor his rivals is less then the supply. If the demand of rivals is lessthan the supply or units available then the difference is to be clinchedto the bidder. Any unit clinched is said to be awarded to the bidder.Actually the bidder’s quantity too does not depend on his action, bid,too. As the process implies this is a dynamic auction.

III-Epmrical StuddiesLambson et al.(2003) studied Seatle Fur Exchange as asequential auctions model. Lots of fur are arranged so as to be theindifferent to bidders and then these lots of furs are auctionedsequentially. They studied the so-called declinng price anomaly whichstates the case that for sequential auctions price must be nonincreasing. Without loss of generality we can consider two units beingauctioned. The authors formally proves that outcome of a sequentialauction will be of three type: 1) both unit being sold to the same buyer2) the units are sold to different buyers at the same price 3) both unitsare sold to the same buyer but at different prices, the price of thesecond being no more than the price of the first.Donald et al.(2006) offered an empirical model of the multi-unitSequential Clock Auction for the right of export permits for timberheld in the Krasnoyarsk Kray of Russia, in the structural model theydeveloped an algorithm that allows to calculate the expected winningprice for each unit sold. This algorithm forms the cornerstone of asimulation-based, structural-econometric strategy to estimate theparameters of both the participation process and the distribution oflatent valuations using commonly available data. They demonstratedthat the approach is feasible by applying it to data from a smallsample of multi-lot, sequential, English auctions of export permits fortimber held in the Krasnoyarsk Kray of Russia.Hortacsu tried to investigate these differences for the Treasurybills for Turkey.

V-ConclusionsMulti-good auctions differ from single-good auctions in essentialways. Most fundamentally, the efficiency result of the second-priceauction for a single good does not carry over to the uniform-priceauction for many goods. In a uniform-price auction for many goods,winning bidders affect the market price with positive probability.Hence, bidders have incentive for demand reduction, upsetting boththe strategic simplicity and the efficiency of uniform-price auctions. Byshading one's bid for additional units, the bidder is able to reduce theexpected price paid on the first units. The more units one buys, thegreater the incentive to shade. As a result, large bidders willsometimes lose additional units to small bidders, even when the largebidders value these units more, creating an inefficiency. This intuitionis easily understood by economists. Indeed, it is equivalent to thebasic result of monopoly — that a monopolist's marginal revenue curvelies below the demand curve. Yet there has been no formalization ofthis intuition in the auction literature. It is possible to see manyacademicians having some misunderstanding for some concepts.In this paper I presented a brief literature review in the field ofmulti-unit auction, which is considerably a new subfield. It is amazingto see how the results can be so different from single good auction.REFERENCES1-Ausubel. Lawrance M. “An Efficient Ascending-Bid Auction forMultiple Objects “The American Economic Review, ( 2004).

3- Milgrom, Paul R.” A Theory of Auctions and Competitive Bidding”Econometrica (1982a).5-Weber, Robert J. “Multiple–Object Auctions” Working Paper (1981)7-Hortacsu, Ali. “Mechanism Choice and Strategic Bidding in DivisibleGood Auctions:An Empirical Analysis of the Turkish Treasury AuctionMarket” (2002)8-Milgrom, Paul. R. “Putting Auction Theory to Work”. Cambridge,England:Cambridge University Press (2004).10-Lambson, Val E. and Thurston, Norman K. “ Sequential Auctions:Theory and Evidence from the Seatle Fur Exchange” (2003)11-Ausubel, Lawrence M. and Cramton , P. “Demand Reduction andInefficiency in Multi-Unit Auctions” (1998)12-Ausubel, Lawrence M. An Efficient Ascending –Bid Auction forMultiole objects , the American Economic Review (2004).13-Donald, Stephan G. Paarsch, Harry J. and Robert J. “An EmpricalModel of the Multi-Unit Sequential, Clock Auction” J. Appl. Econ.(2006)