Auctions. MSc Finance Theory of Finance 1: Financial Topics Autumn Arup Daripa Birkbeck College. The background

Transcription

1 Auctions MSc Finance Theory of Finance 1: Financial Topics Autumn 2005 Arup Daripa The background Selling through an auction is an old idea Sotheby s founded in 1744, Christie s founded in Posting a price is a good way to sell if the seller has a clear idea about demand The advantage of an auction is that the seller does not need to have an idea about the value of the good to consumers 2 1

2 The background However, holding an auction is costly Result: Only high value items are sold through auctions The internet has expanded the scope for auctions enormously Bidders can place bids at different times Bidders do not need to be at the same place 3 Fees The offline and online fees give an indication of the cost advantage of online auctions Sotheby s (offline) charges the buyer and seller 15% and 20% (respectively) of the final price ebay charges only the seller a fee of about 5% of final price (of course, this is a lower quality service) 4 2

3 Auction Theory To analyze auction theory, we need to classify auctions according to the valuation environment the format of the auction (i.e. rules such as how to bid, who wins, what the winner pays) 5 Valuation The value of a bidder is his/her maximum willingness to pay If a bidder has value v for an object, and bids price p, and wins, the payoff is (v-p) There are 2 basic valuation environments 1. Private values 2. Common values 6 3

4 Valuation Environments Private values: Different bidders have different values. The value of each bidder is unrelated to the values of other bidders. One bidder might like a painting, but another might not. Note that one bidder might have a high value, and another might have a low value. Thus the value to the winner depends on who wins the auction. 7 Private Values Suppose there are two bidders bidding for an object, one with value 10 and another with value 5 If the bidder with value 10 wins, the outcome of the auction is efficient. If the bidder with value 5 wins, the outcome of the auction is inefficient. 8 4

5 Common Values Common Values: The value to the winner is the same no matter who wins the auction. This value is unknown to bidders. Each bidder must try to guess the value. Example: auction for the right to any oil under a specific plot of land Example2: Suppose there is a jar full of 1 coins on a table, and this is being auctioned. 9 Auction Formats 4 basic formats English auctions (Christie s, Sotheby s) Sealed bid first-price auctions (tenders) Dutch auctions (Tulips in Holland) Sealed bid second-price auctions (Vickrey auctions) 10 5

6 Vickrey auction and English Auction Suppose a painting is being auctioned and there are 5 bidders with values (in 100,000 units) 8, 6.5, 5, 2.5, 2. In an English auction, price rises continuously, and the auction price is equal to 6.5 In a Vickrey auction, bidders submit sealed bids, the highest bidder is the winner and pays the second highest bid 11 Vickrey auction and English Auction If bidders have privately known values that are independent of each other, we say that the setting is one of Independent Private Values (IPV) In an IPV setting (e.g. most auctions for art, antiques and collectibles) Vickrey auctions and English auctions are equivalent 12 6

7 First-Price and Dutch Auctions In a First-Price Sealed Bid Auction (usually simply called First-Price auction), the highest bidder wins and pays his/her own bid. In a Dutch Auction, The auctioneer calls a high price and then gradually lowers the price The bidder who first says stop wins and pays the stop out price 13 First-Price and Dutch Auctions In a sealed bid first-price auction, a bidder has to decide how much to bid, without knowing what others are bidding. In a Dutch auction, a bidder must decide where to stop, without knowing where others plan to stop. Formally, a bidder s bid in a first-price auction is the same object as a bidder s stopping price in a Dutch auction. Result: Dutch auction and First-Price auction are the same (result in same auction price) no matter what the auction environment is. 14 7

8 Summary Under independent private values, English auction = Vickrey auction Under IPV, as well as other auction environments Dutch auction = Sealed bid first-price auction 15 Revenue Equivalence But which auction (Vickrey or first-price) is better for the seller? Revenue Equivalence Theorem: Under IPV, all four auctions generate the same revenue for the seller. 16 8

9 Bidding in a Vickrey Auction Suppose there are 2 bidders. Bidder 1 has value V and must decide the best bid. Suppose the best bid is b. Consider 3 possibilities: b<v or b = V or b>v 17 Bidding in a Vickrey Auction STEP 1 Compare a bid b<v to a bid b=v Let B2 be the other bidder s bid. There are 3 possible cases as follows. 18 9

10 Bidding in a Vickrey Auction Step 1 B2 V V V B2 Bid V Bid b b b b B2 0 case1 case2 case3 0 0 V B2 V B2 0 V B Bidding in a Vickrey Auction STEP 2 Compare a bid b>v to a bid b=v There are, as before, 3 cases as follows

11 Bidding in a Vickrey Auction Step 2 B2 b b b B2 V V V B2 0 case1 case2 case3 0 0 Bid V Bid b 0 0 V B2 V B2 0 V B2 21 <0 Bidding in a Vickrey Auction Thus we have the surprising conclusion that under a Vickrey auction, the best way to bid is to simply bid your true value (i.e. your maximum willingness to pay) Therefore truthful bidding is optimal in an English auction under independent private values 22 11

12 Bidding in a First-Price Auction In a First-Price auction, bidders do not bid true values each bidder shades his bid so that it is below his value 23 Caveat! In auction design, details matter should not blindly apply auction theory If there are very few bidders and bidders are likely to be very asymmetric (e.g. one bidder has a high value, but others have low values), a second-price auction might not work very well 24 12

13 Example of Design Failure New Zealand Spectrum auction New Zealand used a second-price auction to sell radio spectrum No reserve price was imposed The outcome was as follows High Bid Second Highest Bid NZ $100,000 NZ $6 NZ $7 million NZ $5000 Source: John McMillan, Selling Spectrum Rights, J. of Econ. Perspectives, Summer 1994, quoted in R. Preston McAfee Auction Design Autumn for the 2005, Real World 25 New Zealand Spectrum Auction The government should either have used a reserve price Or some other auction format Such failures constitute a public subsidy to the winning company 26 13

14 Common Value Auctions In a common value auction, the actual value of the object being auctioned is the same to all bidders but the actual value is not known to anyone Bidders place bids on the basis of their estimate of the actual value Example: oil lease auctions 27 Common Value Auction In this case, the value of a bidder is simply his estimate, and now values are likely to be strongly positively correlated When the actual value is high, bidders will tend to have higher estimates When the actual value is low, all bidders are likely to have lower estimates The technical term for such correlation is affiliation 28 14

15 Winner s Curse Winner s curse is the idea that the winner is the bidder with the highest estimate and this might well be an overestimate Thus upon winning, the winner might find out that he paid more than the object is worth 29 Winner s Curse and Bidding Behaviour In deciding what to bid, the bidders must take winner s curse into account The presence of winner's curse makes bidders more conservative

16 Revenue and the Number of Bidders Does the seller get a higher revenue as the number of bidders go up? Private Value auctions yes. Common value auctions not necessarily. There are 2 effects the competition effect and the winner s curse effect 31 Revenue and the Number of Bidders The first effect induces more aggressive bidding, but the second induces less aggressive bidding Both effects increase as the number of bidders rises 32 16

17 Revenue Ranking An auction generates greater revenue for the seller if the payment of the winning bidder has greater linkage to the value estimates of other bidders. In other words, if bidder s can base their final payment on other peoples information, they feel more confident about bidding - and thus less conservative in bidding 33 Revenue Ranking In a sealed-bid first-price (or Dutch) auction, there is no such linkage (winner pays own bid). This auction has the lowest revenue. A sealed-bid second-price auction (Vickrey auction) has more linkage since the winner pays the second highest bid - which is linked to the value estimate of the second highest bidder

18 Revenue Ranking The English auction has the greatest linkage between the payment of the winning bidder and the value estimates of other bidders since bidding is open, and each bidder can learn by observing other bidders' bids This generates the most revenue 35 Revenue Ranking Thus Revenue from English > Revenue from Vickrey > Revenue from First Price (as well as Dutch) 36 18

19 Online Auctions We now explore some interesting microstructure features of online auctions We start by examining the popularity of English auctions, the nature of goods and services being sold, how listing sites operate 37 Online Auction Formats (survey: 142 sites, some with multiple formats) English Sealed Bid FP/SP Dutch 121 Source: Lucking-Reiley Auctions on the internet Continuous Trading Double 38 auctions 19

20 Why is the English Auction so Popular? Performance under private values Performance under common values Simple bidding strategy However, problem of sniping Extended end time one solution Proxy bidding a second solution Works under private values 39 Proxy Bidding Under Common Values Some high-value antique auctions are common value auctions Inexpert bidders will try to learn from the behaviour of expert bidders How would you expect the experts to bid? Should proxy bidding work? 40 20

21 What is being sold? Initially, the largest category was collectibles (why?) Increasingly, goods and services traditionally sold through posted prices are also being offered through online auctions A principal reason is that online auctions serve as a device to enable price discrimination which allows sellers to reach the lower end of demand. 41 Business Models of Online Auctions The two primary business models are those of merchant sites and listing sites Merchant sites offer own goods for sale Listing sites act as agents for other sellers, and derive income from fees charged to sellers and buyers 42 21

22 The Online Auction Business (Listing sites) Others Amazon 6% 6% Yahoo! 28% ebay 60% ebay Yahoo! Amazon Others Autumn Source: 2005, Hall (2001), Digital Dealing, Texere 43 The Dominance of ebay The dominance of ebay and network effects: Where buyers are, sellers go Where sellers are, buyers go 44 22

23 Minimum Bid (Announced Reserve Price) and Secret Reserve Price A minimum bid (an announced reserve price) is usually present in any auction Minimum bids are important recall the New Zealand fiasco Sometimes a secret reserve price is present as well Most such auctions would say when the secret reserve has been met 45 Minimum Bid (Announced Reserve Price) and Secret Reserve Price What could be the reason for using a secret reserve price? If entry is costly, a secret reserve price is likely to discourage entry In common value auctions, this might be a device to hide the seller s own valuation This might encourage bidding to start at low prices and gradually increase thus reducing winner s curse 46 23

24 Fees The fee charged by listing sites has two main components A listing fee (which depends on the size of the minimum bid) A percentage of the amount of the final bid price (ebay charges 5% of first $25, 2.5% of additional amount upto $1000, 1.25% of any additional amount above $1000) 47 Listing Fees, Reserve Price and Chance of a Sale As noted before, listing sites charge a listing fee There is an interesting connection between the fee and reserve prices A higher listing fee raises the incentive to sell therefore induces sellers to set a lower reserve price improving the chance of selling 48 24

25 Listing Fees, Reserve Price and Chance of a Sale ebay has the highest listing fee, followed by Amazon, followed in turn by Yahoo! (which does not charge any listing fee) The result is as theory predicts: 54% of ebay auctions result in a sale, while 38% of Amazon auctions result in a sale, and only 16% of Yahoo! auctions result in a sale 49 Abuses of Ascending Auctions An ascending auction such as an English auction or its ebay version, can be open to certain kinds of abuses by both bidders and the seller Shill bidding abuse by seller Bid retraction abuse by bidders 50 25

26 Shill Bidding The seller can try to bid up the price In auctions like ebay, this can increase the seller s revenue Of course, this possibility is present in traditional ascending auctions as well, but is magnified in internet auctions Of course, the seller runs the risk of winning himself, and thus needs to shill bid carefully 51 Shill Bidding Seller s reputation matters rating system on ebay This also means that if the seller himself is the organizer of the auction, bidders are unlikely to trust a proxy bidding system 52 26

27 Retracting a Bid (Bid Shielding) In proxy bidding, bidders might have an incentive to put a false high bid (which is then retracted) to reveal the current highest value Putting a false high bid also deters other bidders from competing then the high bid can be withdrawn at the last minute allowing the bidder to win the auction at a low price Need bid guarantees through credit cards 53 Online Bidding Strategies: ebay We start by examining proxy bidding in ebay auctions Next, we look at the problems faced by a standard English auction 54 27

28 Proxy Bidding Imagine another way of bidding in an English auction Instead of going to the auction yourself, you tell your robot the maximum amount you are willing to pay for the object (your value), and send the robot to the auction. Your robot will bid the minimum bid increment over the current top bid until either the top bid exceeds your value (you lose), or you win and pay the second-highest value. 55 Proxy Bidding: Applying Vickrey Auctions The opening bid on an item is 30 and there are no bids. The minimum bid increment is 5 You decide to bid on the item and the top price you will pay is 80. You place a bid for 80, but you will be the current high bidder at 35 Sometime later, another bidder bids 50, but you will still be the current high bidder at 55 Still later, but before the item closes, another bidder bids 90, then they become the current high bidder at

29 Proxy Bidding Under private values, proxy bidding implements a Vickrey auction (second price sealed-bid auction) This is very useful, since the optimal bidding strategy is very simple you simply submit your maximum willingness to pay, thus eliminating the need to maintain a constant vigil ebay (as well as many other auction sites) uses a proxy bidding system 57 Proxy Bidding An ebay auction progresses just as an English auction, but under private values, proxy bidding enables bidders to act as if they are participating in a Vickrey auction (a sealed-bid second-price auction), and submit a bid which is their true value, and bid just once

30 Sniping Auctions on ebay have a hard end-time. This creates a potential problem in an English auction. Bidders might have an incentive to place a bid at the very end, thus preventing anyone else from responding. This is known as sniping. The biggest advantage of proxy bidding under private values is in eliminating the incentive to snipe 59 Sniping The other solution is to eliminate the hard end time and extend the auction for 5 minutes (say) after the last bid. Thus auction ends only if no activity in last 5 minutes This is the solution adopted by Onsale This is not a very good solution since it takes away an important advantage of online auctions that bidding can be asynchronous 60 30

31 Proxy Bidding Under Common Values Some high-value antique auctions are common value auctions Inexpert bidders will try to learn from the behaviour of expert bidders How would you expect the experts to bid? Proxy bidding does not work The only solution to sniping is extension of end time 61 Multi-unit Auctions Bidders submit demand functions With K units, the (K+1)th bid is taken as the market clearing price Two main forms: Discriminatory auctions all bids at or above the market clearing price win, and all winners pay the prices they bid Uniform Price auctions - all bids at or above the market clearing price win, and all winners pay the market clearing price 62 31

32 Multi-unit Auctions Discriminatory auctions are like first price auctions A common misconception is that uniform price auctions are like second price auctions To see this, consider the following simple example: 2 identical units are being auctioned, and there are 2 bidders with private values (10,8) and (7,2) We will name the units unit 1 and unit 2 63 Multi-unit Auctions In a uniform price auction, will the bidders bid their true values? Suppose they do. Then the market clearing price is 7, and bidder 1 s payoff is (10-7) + (8-7) = 4 Now suppose bidder 1 deviates and while he bids 10 on unit 1, he does not submit any bid on unit 2 (i.e. submits a bid of 0 on unit 2) The new market clearing price is 2 (which is now the third highest bid), and bidder 1 s payoff is 10-2 = 8. Thus the deviation is beneficial, showing that the bidders do not optimally bid true values

33 Multi-unit Auctions The correct generalization of Vickrey auction is as follows: Consider the market demand excluding bidder 1 s demand. Now for each unit that bidder 1 s bid replaces, the price paid must be the replaced bid. In the example above, the market demand excluding bidder 1 s demand is (7,2). Now introduce bidder 1 s bid on the first unit, which is replaces 2, so bidder 1 wins this unit and pays 2. Now introduce bidder 1 s bid on unit 2, which is 8. 8 replaces 7, so bidder 1 wins the second unit as well and pays 7. Thus total payoff of 1 is (10-2) + (8-7) = 9. In this auction, bidders bid true values. 65 Multi-unit Auctions Similarly, if the values are (10,6) and (7,2), first consider the market demand without 1 s demand. This is (7,2). Now introduce 1 s demand. First, 10 replaces 2, so 1 wins unit 1 and pays 2. But 6 fails to replace 7 so bidder 1 does not win unit 2. Similarly, consider the market demand without 2 s demand. This is (10,6). Now introduce 2 s demand. 7 replaces 6, so 2 wins unit 2 and pays 6. But 2 fails to replace anything so bidder 2 does not win any further units

34 Multi-unit Auctions Thus bidder 1 wins a unit, pays 2 and bidder 2 wins a unit, pays 6. This example also shows why multi-unit Vickrey auctions are politically problematic different bidders might have to pay very different amounts on different units in particular a bidder bidding more pays less. 67 Multi-unit Auctions There are several important applications of discriminatory and uniform price auctions. Treasury auctions in several countries Repo auctions for selling money used by Bundesbank, European Central Bank Telecom auctions in several countries Auctions for corporate bonds Hambrecht s OpenBook auction Auctions for stocks OffRoadCapital IPO auction Hambrecht s IPO auction 68 34

35 Telecom Auctions Economists have been advocating auctioning radio spectrum since 1960s The US Federal Communications Commission was the first to auction radio spectrum for phone licences in 1994 The auction raised $20 billion twice the original estimate The UK s 2G mobile-phone licences were awarded using a beauty contest Finally, in 2000 UK auctioned off 3G licences 69 Auctions vs Beauty Contests A well designed auction is most likely to allocate objects to those who can use them most valuably Beauty contests rely on government bureaucrats to assess the merits of competing firms business plans An auction forces companies to put their money where their mouths are Thus an auction can extract information otherwise unavailable to the government 70 35

36 Auctions vs Beauty Contests Beauty contests are opaque and open to favouritism and corruption The Spanish and Swedish 3G beauty contests provoked litigation and substantial political debate An auction can raise a lot of money - the UK auction generated 2.5% of GNP (enough for 400 new hospitals) Beauty contests provide huge public subsidies to companies obtaining licenses 71 Auctions vs Beauty Contests A common objection to auctions is that the consumers would pay higher prices later This is not correct, as sunk costs do not affect prices Another way to see this is to ask would companies charge lower prices if they were given the licences for free? 72 36

37 Auction Design: Practical Concerns Main Design Concerns: Collusion and Entry Ascending auction not good for attracting entry, weaker bidders discourages. Ascending auction also can generate collusion easily Sealed-bid auction better for attracting entry, less incentive to collude However, in a sealed-bid auction, less information is revealed in the course of the auction an ascending auction allows bidders to feel more comfortable with their bids 73 Auction Design: Practical Concerns Other Concerns: Reserve prices Political problems Loopholes Credibility Market structure 74 37

38 Auction Design: Practical Concerns The main lesson is that one size does not fit all. Details of particular auction circumstances matter a great deal Designing auctions without paying sufficient attention to such details can lead to disaster The UK 3G telecom auction were designed by experts, and was a great success 75 Auction Design: Practical Concerns Most auctions in European countries were poorly designed, and sometimes failed badly, while some countries just got lucky because the bidders were given bad advice by so-called experts

39 UK Telecom Auction A simultaneous ascending auction was used in the US to sell telecom licences Initially, in the UK, only 4 licenses were available. The proposed design reflected the practical problems of collusion, entry as well as information revelation. The proposed design was as follows: Use an ascending auction to eliminate all but 5 bidders Then have a sealed bid discriminatory auction to allocate the licenses 77 UK Telecom Auction However, engineering advice changed later on and 5 licenses became available. The design problem became simpler. A design similar to the US design was finally used in the UK with the added restriction that a bidder could not win more than 1 licence The UK auction offered 5 licenses. There were 4 incumbents (Vodafone, Cellnet, Orange, One-2-One). The presence of the 5 th licence attracted entry by others 78 39

40 Revenues from European 3G Mobile Spectrum Auctions Year 2000 auctions UK Netherlands Italy Switzerland per capita Year 2001 auctions Belgium Greece Denmark per capita Germany Austria Source: Klemperer, Conclusion It is important to understand basic auction theory In more complex settings, design of auctions is a critical issue, and straightforward reliance on received theory makes for poor design In such cases it is important to remember that one size does not fit all, and the design must be based on details of auction circumstances 80 40