Cxn, A Case Study

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This case study outlines the workings of the Consumer Exchange Network, or CXN
(www.cxn.com). CXN is a St. Louis, MO-based startup company with the mission of
providing an efficient online pricing mechanism to bring together buyers and sellers of
new consumer products.

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Cxn, A Case Study

  1. 1. CXN: A Case Study Carrie Beam Gene Fusz The Fisher Center for Management, President, CXN Information and Technology 925 N. Lindbergh Blvd Haas School of Business St. Louis, MO 63141University of California, Berkeley genefusz@cxn.com Berkeley, CA 94720 beam@haas.berkeley.edu CMIT Working Paper 97-WP-1025 October 14, 1997
  2. 2. Table of Contents1 Introduction............................................................................................................. 12 Background ............................................................................................................. 13 Designing the Exchange Environment ..................................................................... 3 3.1 Starting with the Traditional English Auction ...................................................... 4 3.2 Departing from the English Auction: Major Differences ..................................... 5 3.3 Supporting a New Auction with Information Technology .................................... 6 3.4 Comparing the Traditional English Auction and CXN ......................................... 74 Value Added from the Information System.............................................................. 85 Conclusions and Areas for Further Research............................................................ 96 Appendix............................................................................................................... 10 List of TablesTable 1 Initial Sequence of Transactions ...................................................................... 10Table 2 Seller and Buyer Agree to Close Sale............................................................... 11Table 3 The Seller Cannot Deliver the Merchandise ..................................................... 12Table 4 The Buyer Changes His Mind.......................................................................... 12
  3. 3. AbstractCXN is a startup company which is designing an Internet-based exchange mechanism tosell new consumer products (such as televisions) in a new and efficient manner. Itintroduces a variant of the standard English auction, in which sellers are the bidders andthe single buyer is the auctioneer. CXN uses information technology and the Internet todepart from standard English auction methodology. Major differences include thesupport of asynchronous bidder participation, the continuously running auction, and theability to auction off multiple items in a succession of single-item sales. Additionally, theInternet provides a broader audience and grants some degree of immunity from rings ofbidders.1 IntroductionThis case study outlines the workings of the Consumer Exchange Network, or CXN(www.cxn.com). CXN is a St. Louis, MO-based startup company with the mission ofproviding an efficient online pricing mechanism to bring together buyers and sellers ofnew consumer products.Gene Fusz, the President of CXN, called Carrie Beam of the Fisher Center in the springof 1997 to discuss the workings of the new business. This case study has come out of thecollaboration between Gene and Carrie. CXN is currently in beta testing. The site offerscamcorders only at this point in time, and is looking for further funding before itbroadens its offerings.2 BackgroundCXN grew out of a desire to bring buyers and sellers of new branded consumer products,such as televisions and VCRs, together in an efficient manner. Consumer products aresold on the “Big Board.”CXN is an Internet-based exchange environment which sells new consumer productsthrough a patent-pending auction mechanism. Because it provides no warehousing,transportation, or advertising, it hopes to provide buyers with a more efficient and lessexpensive environment than the traditional consumer products superstores, such as Fry’sElectronics or Best Buy. While business-to-business procurement is certainly notexcluded, CXN currently targets individual buyers and attempts to match them withcorporate sellers. The corporate sellers could include (but are not limited to) currentsuperstores, importers, and warehouses.Briefly, this is how CXN works. Both buyers and sellers are anonymous until a sale hasbeen made, at which time CXN provides the parties the information necessary tocomplete the sale. 1
  4. 4. From the seller’s point of view, CXN works as follows. First, seller joins the CXNnetwork for one-time member registration fee of $25 or less. Second, the seller purchasesan offer posting certificate; the certificate details the type of merchandise offered and theoffering price. The price of the certificate depends on the asking price of themerchandise being sold, and will be from $1-$10 for products costing from $50 to $1000.Third, the seller’s offer becomes visible to buyers only if it’s the lowest priced offer. If abuyer chooses to purchase the seller’s merchandise, CXN will provide each party withinformation necessary to contact the other, and the trade is arranged.1From the buyer’s point of view, CXN works as follows. Buyers must first join the CXNnetwork by paying a one-time new member registration fee of $25 or less. A buyerinterested in a new color television will then locate the product on the CXN menu. Thebuyer will see only the lowest price offered nationwide, a price which was determined bythe auction environment in which several sellers bid against each other.2 Theenvironment was designed to make the buyer’s experience as simple and easy as possible.The buyer will then purchase an option for $10, which locks in the price for that productfor one day (8 full business hours). CXN provides the buyer with information necessaryto contact the seller, and the trade is arranged.A preliminary sellers’ bidding screen design is shown below in Figure 1. This screen isavailable only to sellers, and it shows the seller the differing price levels, as well as thequantity available at each price. Buyers only see the lowest price offered – in this case,$200 for the television. Figure 1 Preliminary Screen Design Sony 19” Color TV Quantity Available Timestamp $210 10 4/2/97 $205 42 3/25/97 $200 35 4/2/97 $200 4 4/1/97 3 $1951 To protect buyer privacy, currently CXN provides the buyer’s name and email address only to the seller.In addition to the seller’s name and email address, the buyer receives the seller’s telephone number, faxnumber, company name and address, contact person, and, where appropriate, driving directions.2 Currently, shipping costs are not included. They average $10-$20 on a several-hundred-dollar camcorder.CXN plans to have ZIP code functionality which determines buyer and seller locations and then addsappropriate shipping costs to the price each buyer sees. Hence, the price an individual buyer sees is thelowest price, including shipping, available to her; it may or may not reflect the lowest raw pricenationwide. This is an important part of CXN’s offerings; however, in the interests of simplicity this casestudy deliberately excludes the ZIP code when formulating the basic model. It assumes instead shippingand handling costs are the same from all sellers to all buyers. The offering prices on the CXN exchange donot include sales tax.3 There is no current offer at $195; the lowest current offer is $200. The $195 is there to make it moreinviting for the sellers to move down to the next level. 2
  5. 5. Items are sorted (and hence offered to buyers) first by lowest price, and then by earliesttimestamp. Several sellers may be at each price level; in that case, CXN relies uponslight differences in timestamp to differentiate them. Each seller may offer a single itemfor sale by purchasing a single offer posting certificate. Each seller may also offer anentire lot of identical items at the same price by purchasing a single offer postingcertificate and choosing the automatic renew feature, to purchase another offer postingcertificate when the first one sells. An important feature of the CXN process is theguarantee – all offers to buy and sell are guaranteed by a deposit. While the processoutlined above is the basic one, there are more details available in Section 6, theAppendix, including what happens if the buyer backs out of a deal or the seller cannotdeliver as promised.CXN makes its money from new member registration fees, from offer posting fees paidby sellers, and from advertising.4 The buyer’s lock-in option money goes to the sellerupon successful completion of the sale. Before the offering price of a piece ofmerchandise is made available to buyers, however, it requires a live, valid offer postingcertificate. Since sellers are not charged for offer posting certificates until a buyer locksthe item in, there is no need to worry about expiration dates on sellers’ offer postingcertificates.3 Designing the Exchange EnvironmentTogether, we reviewed the design of the exchange environment. The objective was todesign an environment in which different sellers would compete with each other throughan auction mechanism. The competition between the sellers would yield the buyers themost competitive price for each piece of merchandise. Sellers would gain access to amuch larger market than was available locally, and make up in volume of sales what maybe lost in reduction of gross profit per unit sold. Buyers would save time and moneylooking for the best available deal.To fulfill its objective, the environment should: 1. Guarantee each buyer would receive the lowest possible price available on CXN at that point in time 2. Guarantee the lowest-cost seller on CXN at each point in time would receive the sale, hence ensuring efficient trades in the economic definition of the word 3. Take advantage of the dynamic, interactive nature of the Internet 4. Encourage many different sellers to join CXNAssumptions made about the environment and participants were as follows: 1. Each buyer who decides to buy will take the lowest price offered at that instant in time. Hence, while there may be several buyers over the course of a4 Although small at first, advertising revenue will rise as the site gains popularity. Initially, there is norevenue from advertising; once it is fully operational, the company expects the advertising revenue willcontribute substantially to total revenue. 3
  6. 6. business day, at any given instant the multiple sellers are competing for the business of a single buyer. 5 2. A single auction begins immediately after one sale is made, and runs continuously until the next sale is made. Many successive auctions may be run over a given period of time. 3. Each buyer who buys will purchase one item at a time. The sale of two items to the same buyer will be modeled as two successive sales of one item. 4. The bidders (here, the sellers) operate on an independent private values model. Each seller has complete, private knowledge about his own (independent) cost to offer the product.6 5. The purpose of the exchange environment is to employ a mechanism which will encourage the sellers to truthfully reveal the lowest price at which they will offer the items.7 6. The sellers are risk-neutral. 7. The total sale price is a function of the bids alone; there are no contingent payments or additional deals (outside of the lock-in option fee and the offer posting certificate price). 8. It is both an interactive and a dynamic exchange environment.3.1 Starting with the Traditional English AuctionThe first decision was which type of auction to use. There are four major types ofauctions in the literature: the English auction, the Dutch auction, the first-price sealed-bid auction, and the Vickrey auction. While space does not allow a comprehensiveoverview here, for an excellent overview and explanation of these four types of auctions,see Milgrom [8], Smith [10], Vickrey [11], or McAfee and McMillan [7]. For a moretheoretical analysis of the auction environment, see Milgrom and Weber’s paper [9], andfor a more mathematical analysis of auction strategy, see Wilson [12].CXN had decided to offer the items using a type of English auction; this section drawsupon auction theory literature to explain how and why the English auction is a good fitfor the CXN environment. The English auction tends to lead to lower selling prices inthis case, and offers opportunities to use the information technology in new, unique ways.5 While each individual sale is made to an individual buyer, it is the collective purchasing power of manybuyers which will encourage the sellers to join CXN.6 Loosely, an independent private values model says all bidders value the item being sold differently andindependently. The alternative, the common values model, says the value of the item depends not only onthe individual bidder’s private information, but also upon some external factor. A typical common valuesmodel applies when the item being sold is an oil field, in which case the common value, the (unknown)amount of oil available, has an effect on the bidders. Because there is not an unknown value of winning thecontract, but rather each seller has his own known, private cost, the independent private values modelapplies (see McAfee and McMillan [7, p. 705] for more on why the independent private values modelapplies here; for a more comprehensive explanation, see Milgrom’s excellent primer [8]).7 In practice, the exchange environment here will have all sellers except the lowest bidder truthfully revealtheir reservation prices. The lowest priced seller only needs to beat the second-lowest-priced seller. Thisdynamic is exactly parallel to the English oral ascending auction, in which the winner wins the item at thereservation price of the second-highest bidder. 4
  7. 7. The traditional English auction is an open outcry, oral, ascending-bid auction whichbegins with all bidders in the same place at the same time, and ends (usually a short whilelater) when only one bidder is left. While the auction is ongoing, each bidder maycontinuously update her bid, and can do so with knowledge of the current bids of theother bidders. The English auction sells a single indivisible object to one of manybidders, and assigns the object to the bidder who values the object most highly8 at theprice of the second-highest valuation. To this we would add McAfee and McMillan’s“benchmark” auction assumptions [7, p. 706] which state that bidders are risk neutral,hold independent private values assumptions, are symmetric, and that payment is afunction of the bids alone.9 (Although traditional English auctions are between a singleseller and many buyers, and CXN’s auction is between a single buyer and many sellers,the dynamics are theoretically the same. The reversal is valid.)The English auction tends to yield a more favorable average sale price. In an ascendingauction, the traditional English auction yields a higher average sale price than the Vickreyauction, which in turn yields a higher average price than either the Dutch or first-pricesealed-bid auction [9, p. 1095]. This result holds whether the auction is ascending (in atraditional English auction) or descending (like CXN’s), and so the English auction is anexcellent way to achieve the goal of offering buyers the lowest possible price.Additionally, the English auction has a dynamic element to it which is not present insealed-bid auctions. Information technology can be used to exploit this dynamic element,expanding the traditional English auction along the time dimension. This also makes theEnglish auction a good fit for CXN’s purposes.3.2 Departing from the English Auction: Major DifferencesThe English auction provided a good starting place. The next task was to take advantageof the Internet’s special characteristics to further design the sales mechanism. The largestdeparture from traditional auction theory comes in the time element. The Internet freesthe auctioneer from fixed starting and ending times, and instead allows the auction to runcontinuously over time. As stated above, a new auction begins immediately afterpurchase of the last item, and ends each time the buyer purchases an item. Sellers cannotdetermine when this will be.In the traditional English auction, all bidders must participate simultaneously. A bidder’sbest strategy is generally to remain active until the price exceeds her threshold, at whichtime she drops out. Harstad and Rothkopf [5] show that even if dropping out and re-entryis allowed in an English auction, the bidder gains nothing by doing so. The Internettechnology changes the basic assumption that all bidders participate simultaneously.Instead, it allows bidders to participate asynchronously, and to “drop in” and “drop out”of auctions by viewing the auction on a Web browser. It was decided that CXN would8 And hence, the English auction is economically efficient.9 This assumes that no post-sale incentive payments are used. 5
  8. 8. design its sellers’ bidding screens to allow each seller to view the best current bids on apiece of merchandise, and also to view which of those bids are hers. She has the optionto place a new bid, or to revise existing bids.10A second difference between the traditional English auction and the Internet-enabledauction is the time dimension. In the English auction, a single auctioneer auctions theitem – in CXN’s case, it would be the exchange network auctioning off the right to sell asingle unit to a single buyer. There would be no value in placing the second place bid.However, the time dimension of the Internet-based auction means that new bidders (andhence more competition for the sellers) could potentially arrive any minute. Moreover,new buyers can arrive at any time. While each buyer would naturally take the lowestpossible price offered, if the inventory at the extremely low price were exhausted, the“second place” bidder would gain the sale. Hence, in the CXN auction, there can begreat value in being at second, third, etc. place in the sales “pecking order” for thecontinuous auction. The seller screens were designed so each seller could see thepositioning of all bids.A third difference between the traditional English auction and the CXN exchange auctionis how they each handle multiple item auctions. The literature on English auctionsincludes papers on multiple items (see [1-4, 6]). When the items are identical, atraditional English auction (or a Vickrey auction – see [11, p. 24]) will sell the N identicalitems to the N highest bidders at the N+1th highest price. Bidders will have no incentiveto bid further, given they have won some item and all items are identical. However, theauctioneer would ideally like to extract the surplus from each possible bidder – in CXN’scase, the consumers would like to encourage each seller to go as low as possible in price.CXN solves this issue by breaking the multiple item auction into successive singlebuyers, purchasing a single item at a time. CXN allows sellers to place bids to sellmultiple identical items at a given price or at different prices. The winner of the sale isthe seller who has the lowest price at the moment the next individual buyer decides tomake the purchase. The sellers here do not know how many buyers will arrive during thecourse of a day, and hence there is not the security of knowing one is in the top N biddersfor N items. Each seller has an incentive to be the low-price seller to ensure winning thenext sale.3.3 Supporting a New Auction with Information TechnologyIn addition to supporting the dynamic continuous-time element to the auction, theInternet has several characteristics which make it a unique and powerful tool. It hasglobal reach and can handle asynchronous transactions. It has a broad audience, and can10 The seller can revise existing bids subject to the following restrictions. A new bid must remain up for atleast 24 hours, and in the initial 24 hours, the seller cannot change the bid to a higher price, nor can theseller cancel the bid in its initial 24 hours. These restrictions apply both to new bids and to newly loweredbids. 6
  9. 9. transmit data quite inexpensively. Additionally, Web browsers and other graphical userinterfaces make it relatively easy to use.These capabilities will benefit CXN in three major ways. First, the Internet will bring ina larger number of sellers. Second, the Internet will help CXN to run a continuous,asynchronous auction mechanism. Third, English auctions are often susceptible to ringsof bidders, and the anonymity chosen by CXN and allowed by the Internet should reducethat likelihood.The Internet is useful to bring in a larger number of potential bidders than couldrealistically be assembled in single place for the sale. Since it allows any seller to joinand offer merchandise at any time, the Internet also lends a bit of uncertainty to the exactnumber of sellers competing at any one time. Furthermore, the ease of use of most Webbrowsers, and the general connectivity of the Internet will allow many sellers, even thosenot very technologically advanced, to participate in CXN relatively easily. In general,with auctions, raising the number of bidders yields a more favorable price for theauctioneer [7, p. 729]; the hope is the Internet will bring in a large number of sellers andgive the buyers extremely favorable pricing.Second, the Internet will help CXN run a continuous, asynchronous auction. Byaccepting bids from sellers at any time of day, and allowing buyers to take advantage ofthese offers around the clock, CXN will be able to continuously update the exchangeprices, again making it simple for consumers to buy items here.Third, traditional English auctions are susceptible to rings of colluding bidders [8, p. 18].In such a ring, the bidders agree to elect one member of the ring to participate in theEnglish auction, bidding up to the ring’s (highest) reservation price; if the item is won,the members re-auction the item among themselves. The capability made possible by theInternet will prevent such types of rings from forming, because the bidders (sellers) donot know each others’ identity. Only seller quantities and prices are revealed, hencemaking collusion nearly impossible.3.4 Comparing the Traditional English Auction and CXNFigure 2 summarizes the similarities and differences between the CXN auction and atraditional English auction: 7
  10. 10. Figure 2 Comparison between traditional English auction and CXN Similarities Traditional English auction and CXN One auctioneer, several bidders Single, indivisible unit for sale Independent private values model for bidders Bidding level and number of active bidders continuously displayed while auction is ongoing Bidders assumed risk-neutral Differences Traditional English auction CXN Auction has distinct beginning and end Auction is continuous; bidders may “drop in” and “drop out” at will Known number of bidders in each Number of bidders is unknown and auction potentially quite large No value in being runner-up Potential large value in being second- or third-place bid, for when winner sells out of inventory Bidders typically know less about true Bidders typically know more about true value of item than does auctioneer value of item than does auctioneer Vulnerable to rings of bidders Less vulnerable to rings of bidders4 Value Added from the Information SystemThe information systems capability provides CXN with the opportunity to add morevalue for sellers also. In addition to reducing the selling costs and allowing access to alarger market of consumers, CXN can offer information technology capabilities. A feware detailed here.After a buyer has purchased an option to lock in the offering price offered by a givenseller, that particular offer posting certificate is considered used. To offer another pieceof merchandise to another buyer, the seller needs a new offer posting certificate. CXNoffers its sellers the ability to automatically renew their offer posting certificates upon thesale of a piece of merchandise. This allows the seller to purchase a new offer postingcertificate to keep the rest of the offers “live” and visible to buyers.CXN offers a “My Office” feature which allows a seller to view her own current offers tosell and the status of current transactions. 8
  11. 11. 5 Conclusions and Areas for Further ResearchCXN presents an interesting preliminary case study. It plans to provide an online auctionenvironment which will change the way consumer goods are bought and sold. It offersguaranteed transaction services, so that each offer to buy or sell must be guaranteed by asmall deposit which is forfeited if the transaction is not carried out as planned. It reversesthe traditional English auction, offering instead an auction which has sellers compete tooffer buyers the lowest price.This is only a preliminary case study writeup. Many further research and practicalbusiness issues remain, and many can only be addressed once CXN is up and working.The actual dynamics of bidding and seller strategy will be interesting and informative.How do sellers bid? Do they follow the independent private values model? Is thereaffiliation between seller offers? What is the seller’s optimal strategy? The other side ofthe coin will prove interesting as well. What is the bidder arrival process? Can it bemodeled as a Poisson process, or is some other stochastic model more appropriate? CXNis in a unique place to capture such dynamic information about the bidding and salesprocess because of its electronic commerce systems and databases.The practical business side of the case study is also of interest. Is CXN viable? Willconsumers actually buy products online instead of choosing to go to local, moreexpensive stores? Will sellers actually choose to offer products online, or will they opt toremain in local businesses? Will warehouses, importers, or other middlemen becomeinvolved?It will be quite interesting to see what the outcome of this startup business venture willbe. 9
  12. 12. 6 AppendixThe appendix details the workings of the buy and sell certificates for participants on theexchange. The most important concept is that offers to buy and sell on CXN areguaranteed by a deposit.Variables: $c price of offer posting certificate bought by seller. This depends on theprice of the merchandise offered, and is not determined until the merchandise is actuallysold. $p the seller’s bid price for the merchandise $g the seller’s guarantee $L fee of buyer’s lock-in optionThe sequence of events is as follows, and assumes the buyer and seller have alreadyjoined CXN by paying the one-time new membership fee. Additionally, the seller has setup the appropriate accounts with CXN.Table 1 outlines the money which has changed hands so far: Table 1 Initial Sequence of TransactionsDescription Seller CXN Buyer1. The seller offers the item for sale2. The buyer sees the item and decides to purchase it.3. The buyer purchases a lock-in option +L -L from CXN for $L.4. The seller gives CXN a (refundable) -g +g guarantee of sale $g.5. CXN gives the buyer the seller’s information and the buyer contacts the seller.11TOTAL –g g +L -L11 The buyer should contact the seller within 24 hours of receiving the seller information. Within 24 hoursof being contacted by the buyer, the seller should provide evidence of delivery (either physical delivery iflocal, or a shipping number if not.) 10
  13. 13. At this point, the transaction will proceed in one of three ways: A. The seller can deliver the merchandise and the buyer pays (shown in Table 2) B. The seller cannot deliver the merchandise (shown in Table 3) C. The buyer changes his mind and decides not to exercise his option to buy (shown in Table 4)A. The seller can deliver the merchandise and the buyer pays Table 2 Seller and Buyer Agree to Close SaleDescription Seller CXN BuyerTOTAL after Step 5 above: -g g+L -L1. The buyer pays the purchase fee to the +p -p seller, usually by credit card over the telephone2. The seller delivers the merchandise to -Item +Item the buyer3. CXN refunds the seller’s guarantee +g -g money4. The seller is charged the offer posting -c +c certificate fee (determined by sale price p)5. CXN gives the buyer’s lock-in option +L -L money to the seller.12TOTAL (L-c) + +c Item – L (p-Item) -p12 The buyer’s lock-in money is transferred to the seller one business week (five business days) after theinitial purchase by the buyer. CXN holds the money for those five days. 11
  14. 14. B. The seller cannot deliver the merchandise Table 3 The Seller Cannot Deliver the MerchandiseDescription Seller CXN BuyerTOTAL after Step 5 above: -g g+L -L 6. The seller is unable to deliver the merchandise to the buyer 7. CXN forwards the seller’s -g +g guarantee money to the buyer 8. CXN refunds the buyer’s lock-in -L +L option money to the buyerTOTAL –g +gC. The buyer changes his mind and forfeits the lock-in option money. Table 4 The Buyer Changes His MindDescription Seller CXN BuyerTOTAL after Step 5 above: -g g+L -L 5. CXN forwards the buyer’s lock-in +L -L option money to the seller 6. CXN refunds the seller’s +g -g guarantee money to the sellerTOTAL L -L 12
  15. 15. References[1] Beam, Carrie, “Auctions on the Internet: An Application of Operations Research to Electronic Commerce,” Department of Industrial Engineering and Operations Research, University of California, Berkeley, Berkeley, CA Qualifying examination, November 11 1996.[2] Burns, Penny, “Market Structure and Buyer Behaviour: Price Adjustment in a Multi-Object Progressive Oral Auction,” Journal of Economic Behavior & Organization, vol. 6, pp. 275-300, 1985.[3] Demange, Gabrielle, David Gale, and Marilda Sotomayor, “Multi-Item Auctions,” Journal of Political Economy, vol. 94, pp. 863-872, 1986.[4] Engelbrecht-Wiggans, Richard and Robert J. Weber, “An Example of a Multi- Object Auction Game,” Management Science, vol. 25, pp. 1272-1276, 1979.[5] Harstad, Ronald M. and Michael H. Rothkopf, “An Alternating Recognition Model of English Auctions,” Rutgers University, New Brunswick, NJ Unpublished working paper, February 1994.[6] Hausch, Donald B., Michael H. Rothkopf, Elmer Dougherty, and Marshall Rose, “Multi-Object Auctions: Sequential vs. Simultaneous Sales/Comment,” Management Science, vol. 32, pp. 1599-1612, 1986.[7] McAfee, R. Preston and John McMillan, “Auctions and Bidding,” Journal of Economic Literature, vol. 25, pp. 699-738, 1987.[8] Milgrom, P., “Auctions and Bidding - a Primer,” Journal of Economic Perspectives, vol. 3, pp. 3-22, 1989.[9] Milgrom, Paul R. and Robert J. Weber, “A Theory of Auctions and Competitive Bidding,” Econometrica, vol. 50, pp. 1089-1122, 1982.[10] Smith, Vernon L., “Auctions,” in The New Palgrave: A Dictionary of Economics, vol. 1, J. Eatwell, M. Milgate, and P. Newman, Eds. New York, NY: The Stockton Press, 1987, pp. 138-144.[11] Vickrey, William, “Counterspeculation, Auctions, and Competitive Sealed Tenders,” Journal of Finance, vol. March, pp. 8-37, 1961.[12] Wilson, Robert, “Chapter 8: Strategic Analysis of Auctions,” in Handbook of game theory with economic applications, R. J. Aumann and S. Hart, Eds. New York, NY: North-Holland, 1992. 13

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