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Auctions

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Types of Auctions I

English Auction (ascending-bid):Initial bid set at seller‘s reservation price (reserveprice)bidders bid up, the last bidder gets the good at her bidding priceYou get information about willingness to pay of othersSometimes time limits eBay Deutschland – Der weltweite Online-Marktplatz

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Types of Auctions II

Dutch Auction (descending-bid):Initial price very highPrice is lowered at time intervalsThe first bidder gets the goodUsed for Dutch flower auctions

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Types of Auctions III

Sealed-bid auction:Only one bid per person in a sealedenvelopeFirst-price sealed bid auction: highestbidder receives the good at her statedpriceReverse sealed-bid auctions used for publicprocurement (highways, publicconstruciton)

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Types of Auctions IV

Second-price sealed-bid auction:Vickrey auction

http://nobelprize.org/economics/laureates/1996/index.html

The highest bidder receives the good, butshe has to pay only the price of thesecond-highest bidder

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Why should you want to usean auction to sell something?

Rules of the auction can easily beinfluencedGoods in limited quantities (oftenunique, but not necessarily)Way to elicite willingness to pay form consumersOnline auctions easily done

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Baseline modelBidders are symmetric:

Bidders select bid from the same distribution of possible bidsBut do not necessarily chose the same

Bidders are risk-neutralBids are based on signals from an independent distribution

Private-value auction: everybody values the good (art) differently: my value does not influence yoursCommon-value auction: true value unknown, but all bidderswould value the good alike (oil field)

Each bidder forms expectations about the true value

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Bidding situationb … bidp … pricePrW … probability of winning the auction(b-p) surplusPrW (b-p) … expected profit of a bid

Revenue equivalence therem:All auctions give the same expected revenue to the seller

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Bidding strategiesOnly in English auction bidders learn more aboutreservation prices of the othersBut dominant strategy:

Always bid up to the reservation price (in fact bid one centabove the last bid of the others)Good is sold at reservation price of the second-highestbidder (plus 1c)

Same prediction in second-price sealed bid auction:Dominant strategy to bid the reservation priceVickrey auction is a truth-telling mechanism:

Structure gives an incentive to reveal the true willingness-to-pay.

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Dutch and sealed-bid auction

Strategically similarNo dominant strategy; you have to consider whatthe others are biddingE.g. Dutch, you should not bid your reservationprice, because then no surplus available any more.If distribution of valuations is known, bidders cananticipate bidding.Nash strategy: assume others are behavingrationally; then you should maximze yourexpected profit

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Dutch and sealed-bid auction II

Nash-strategy:Estimate the reservation price of the second-highest bidder and bid it.How to do it?Number of bidders n is important: the morebidders, the closer you should bid to your ownreservation price

If distribution of bids is uniformly distributedbetween L (low end) and v (bidders reservationprice):B = v - [(v-L)/n]

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Strategy for SellerAuctions similar to third-degree pricediscriminationSeller should always sell to bidder withhighest reservation priceAuctions are efficient in that sense

Example: Four units to sell, MC=0Six consumers with WTP (90, 60, 50, 40, 20, 15)Seller posts a price of €40

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Use of auctions to gather moreinformation about buyers

Example: Repurchase Tender Offer(company wants to buy back shares fromcurrent shareholders)One possibility: fix a price, wait how manyshares will come backOr: modified Dutch auction: firm announces a price range; shareholdershave to provide a supply schedulePrice is set afterwards

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•Company assumes share is worth $20

•Expectations about supply schedule of shareholders under three scenarios

•Profit = (20 - share price ) * shares traded

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Expected profit if firm doesnot know supply schedule

Firm has to set a price:

EV(15) = 2.0*0.4+1.55*0.3+1.4*0.3 = $1.685EV(16) = 1.66*0.4+1.6*0.3+1.26*0.3 = $1.522EV(17) = 1.8*0.4+1.245*0.3+1.2*0.3 = $1.453

$15 is chosen

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Expected profit if auction ischosen

Price selected only after the auctionIn strong supply case $15 is chosen, in medium $ 16 and in weak $15EV(auction) = 2.0*0.4+1.6*0.3+1.4*0.3 = $1.700

Profit possible, because firm can set a higher price in one of thecases

How does it work? You need a truth-telling mechanism, so that shareholdersreveal the right supply scheduleContract is needed: shareholders cannot sell more share at the specified price (otherwise they would lie)

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Priceline: an example for a reverse auction

www.priceline.comAuction for airline seatsAirline seats are perishable goods, marginal costs arevery low, empty seats bring no cash

Giving official discounts does not make sense, because pricestructure would suffer

Buyers name price they are willing to pay, priceline isauctioning: if an airline is accepting, the sale isdone(!)

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Risk aversion

In second-price auctions risk-aversion doesnot matter. Why?What in a first-price auction or Dutch auction?

No dominant strategyHigher bids increase probability of winningIf risk-averse bidders want to avoid losing, theywill increase their bid

If bidders can be assumed to be risk-averse, then sellers should chose first-price auctions!!

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Number of bidders

Expected bid (sale) = reservation price of thesecond-highest bidder.More bidders will increase profit for the sellerAssume reservation price of bidders isuniform between 0 and €100, expectedrevenue for seller:B = [(N-1)/(N+1)*(highest reservation price)

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Winner‘s curse

Is it always good to win the auction?Be aware in common value auctions!

True value of the good not known for sure, but common to all (e.g. oil field)Sealed-bid first price auction:

Most optimistic bidder wins

Same problem for project procurement(reverse auction)

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Winner‘s curse

Serious problemWhat can you do?

The less information you have relative to theothers, the lower your bid.The less confident you are, the lower should bethe bid.The more bidders, the lower should be the bid.

This is just the opposite, the typical „gut feeling“ wouldtell you!!

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Problems in auctions (forsellers)

Make the auction attractive for bidders:The more bidders you attract, the betterSetting a start price too high, can deter biddersfrom entering

Collusion of bidders can occurIn particular in multi-unit auctions, where severalunits of a good are soldCollusion is not illegal in auctions in general, but in gov‘t procurement reverse auctions

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Collusion in auctions: paper byPaul Klemperer in Journal of Economic Perspectives, 2002

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Books for summer reading: you will enjoy them!