Auctions. N i k o l a o s L i o n i s U n i v e r s i t y O f A t h e n s. ( R e v i s e d : J a n u a r y )

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1 Auctions 1 N i k o l a o s L i o n i s U n i v e r s i t y O f A t h e n s ( R e v i s e d : J a n u a r y )

2 Common definition What is an auction? A usually public sale of goods where people make higher and higher bids (= offers of money) until the good is sold to the person who will pay most. General economic definition An auction is a method (mechanism) of allocating scarce goods. 2 A method that is: mediated by an intermediary (auctioneer). well-specified (it runs according to explicit rules). based upon competition of self-motivated participants (e.g. sellers wish to obtain as much money as possible while buyers want to pay as little as necessary). efficient in the sense that it usually ensures that resources accrue to those who value them most highly.

3 When are auctions used? Auctions are useful when selling goods of undetermined quality. the goods do not have a fixed or determined market value. i.e. when a seller is unsure of the price he can get. 3 Auctions are more flexible than setting a fixed price. less time-consuming and expensive than negotiating a price.

4 Where auctions are used? Art, antiques, collectibles (e.g. Christie s, Sotheby s) Treasury auctions (bill, notes, bonds, securities) Public procurements Transfer assets from public to private sector (privatizations) Natural resources (right to drill oil, off-shore oil lease) Spectrum rights (telecommunications, television) Private firms sell their products (flowers, fish, tobacco, livestock, diamonds) Internet auctions (ebay, google, yahoo) 4

5 Taxonomy of Auctions 5

6 Auction In an (demand/selling) auction, multiple buyers bid for a good being sold by one seller. 6 b1 b2 s b3 bn

7 Reverse Auction In a reverse (supply/buying ) auction, multiple sellers offer a good that a buyer requests. 7 s1 s2 s3 b sm

8 Double Auction In a double auction, multiple sellers and buyers submit bids. 8 S1 b1 S2 b2 Sm bn

9 Major Types of Auctions English 9 First-price sealed-bid Second-price sealed-bid (Vickrey auction) Dutch

10 English Auction An open ascending sequential bid auction. The auction begins with the lowest acceptable price (the reserve price) Each bidder is free to raise his bid (or auctioneer calls out an increasing series of prices). Bidders observe the bids of others and decide whether or not to increase their bid. The auction ends when no bidder is willing to raise the bid. The item is sold to the highest bidder. 10

11 Dutch Auction An open descending bid auction. 11 The auction begins at an extremely high asking price. The bid decreases until one bidder is willing to pay the quoted price. Bidders observe only the bid of the winner.

12 First-Price Sealed-Bid Auction A simultaneous sealed bid auction. 12 Each bidder submits a bid in a closed envelope. Bidders do not know the bids of other players. The envelopes (bids) are opened at the same time (simultaneously). The bidder with the highest bid wins the object and pays exactly the amount he bid.

13 Second-Price Sealed-Bid Auction A simultaneous sealed-bid auction (Vickrey) 13 The same bidding process as a first-price sealedbid auction. The bidder with the highest bid wins the object and pays a price equal to the second-highest bid (or highest unsuccessful bid).

14 Other (Hybrid) Types of Auctions Multiunit auction Sell more than one identical items at the same time. Combinatorial auction Simultaneous sale of more than one item where bidders can place bids on an "all-or-nothing" basis on "packages" rather than just individual items. Anglo-Dutch auction Begins as an English auction and then turns to a Dutch auction. Amsterdam auction Begins as an English auction. Once only two bidders remain, each submit a sealed bid. 14

15 Other (Hybrid) Types of Auctions All-pay auction All bidders must pay their bids regardless of whether they win. 15 Reserve auction The seller reserves the right to accept or reject the highest bid. Buyout auction An additional price is set (the buyout price) so that any bidder can accept, at any time during the auction, thereby immediately ending the auction and winning the item. Walrasian auction The auctioneer takes bids from both buyers and sellers in a market of multiple goods. Depending on the bids of both buyers and sellers, prices rise or drop. The auction concludes when supply and demand exactly balance.

16 Information Structures 16

17 Information Structures Information about number of bidders Depends on auction mechanism 17 Information about the bids of other bidders Depends on auction mechanism Information about the value of the item being auctioned Independent or interdependent valuations

18 Bidder Valuations: Private Values Each bidder makes his own private valuation of the item for sale. Bidders valuations are determined by personal tastes. Bidders willingnesses-to-pay for the item are distinct (independent). Bidders valuations do not depend on those of other bidders. Goods are acquired for personal consumption. I want it All bidders have private valuations and keep that information private. Bidders know their own valuation of the item, but not other bidders valuations. Any new information learned during the auction: Does not affect valuations Affects only bidding strategies 18

19 Bidder Valuations: Correlated Values Bidders valuations depend on those of other bidders. Bidders are unsure of an item s true value. Bidders willingnesses-to-pay are related to one another (correlated) 19 Bidders do not know their own valuation or the valuations of others. In fact, bidders own valuations depend on those of other bidders. Goods are acquired for resale or commercial use. I am not sure I want it, but others might in the future Bidders use their own information to form a value estimate. The higher a bidder s estimate the more likely it is that other bidders also have high value estimates (interdependent value estimates). Any new information learned during the auction affects valuations and bidding strategies.

20 Bidder Valuations: Common Values Common values is a special case of correlated values. 20 Common values is the case in which the true (but unknown) value of the item is the same for all bidders. The item is really worth the same to all, but the exact amount is unknown.

21 Bidder Valuations: Examples 21 Private Values Private goods such as fish, flowers, diamonds Correlated Values Spectrum Common Values Oil & gas resources Procurements Houses and other properties Treasury bills, bonds

22 Optimal Bidding Strategies 22

23 Optimal Bidding Strategy Bidders bid differently depending upon the rules of the auction Thus, it is worth understanding the rules of an auction thoroughly. 23 A bidder tries to predict the behavior of the other bidders. Each bidder makes an estimate of his own value of the object and also an estimate of what others will bid on it. Good bidding is often the result of correct predictions about the behavior of other bidders Sometimes that means guessing the extent of someone else's information correctly.

24 Optimal Bidding Strategy in an English Auction with Private Values With independent private valuations, the optimal bidding strategy is: bid a small amount more than the previous bid. remain active until the price exceeds own valuation then stop. 24 This is optimal because each bidder always wants to buy an object if the price is less than its value to him, but he wants to pay the lowest possible price. Bidding always ends when the price reaches the valuation of the player with the second-highest valuation.

25 Optimal Bidding Strategy in a Second-Price Sealed-Bid Auction with Private Values The optimal strategy is to bid own valuation of the item. This is a dominant strategy since: Bidding less than true valuation decreases the probability of winning. Bidding more than true valuation increases only the risk of buying the item for more 25 than it is worth to him. If 2 nd bid < own valuation no gain to bid more than own valuation (win and pay 2 nd bid in any case). If 2 nd bid > own valuation increase probability of winning an object that is worth less (incur losses). The existence of a dominant strategy means that each bidder can determine his own bid without regard for the actions of others. The outcome is that the item is awarded to the bidder with the highest valuation at a price equal to the second highest valuation. Second-price sealed-bid auction is strategically equivalent to English auction.

26 Optimal Bidding Strategy in a First-Price Sealed-Bid Auction with Private Values Bidders must decide the maximum amount they will bid. The decision is based upon: Their own valuation of the object. Their prior beliefs about the valuations of other bidders. No relevant information is disclosed in the course of the auction. The tradeoff is: bidding high and winning more often but with lower profit margin. bidding low and benefit from a bigger profit margin if the bid wins. 26 Bidders have an incentive to bid less than their own valuations. The decrease depends on: Competition (number of bidders): Many bidders implies that bids are close to true valuation. Prior beliefs (distribution) of valuations: As lowest expected valuation increases, bids are closer to true values. In practice, most bidders bid an amount equal to one s best guess of the next highest bid (or close to market consensus). This also helps to avoid winner's curse. If there are n bidders who all perceive valuations to be evenly (or uniformly) distributed between a lowest possible valuation of L and a highest possible valuation of H, then the optimal bid for a risk-neutral player whose own valuation is v is v L b v. n

27 Bidding Strategy in a Dutch Auction with Private Values Bidders must decide the maximum amount they will bid. the same problem as in a first-price sealed-bid auction. 27 Dutch auction is strategically equivalent to first-price sealed-bid auction. In practice, if the bidder with the highest interest really wants an item, he cannot afford to wait too long to enter his bid. That means he might bid at or near his highest valuation.

28 Strategic Equivalence 28 Dutch First-Price Sealed-Bid English Second-Price Sealed-Bid

29 Optimal Bidding Strategies with Correlated Values Difficult to describe optimal bidding strategies because Bidders do not know their own valuations of the item Bidders do not know the valuations of others. 29 The auction process may reveal information about how much the other bidders value the object. English auction: Bidders observe not only that other players drop out, but also the price at which the competition abandons the bidding. That tells a bidder a great deal about the valuations of others and allows a bidder to revise his valuation. Optimal bidding requires that players use any information gained during the auction to update their own valuations.

30 The Winner s Curse Winner s curse: A "lucky" winner pays more for an item than it is worth. Auction winners are faced with the sudden realization that their valuation of an object is higher than that of anyone else. 30 The winner is the bidder who is the most optimistic about the true value of the item. To avoid the winner's curse, a bidder should revise downward his or her private estimate of the value to account for this fact. The winner s curse is most pronounced in sealed-bid auctions.

31 The Winner s Curse The winner s curse is greater in Sealed-Bid Auctions Open bid auctions (e.g. English) allow information revelation and upgrade of estimations. The winner s curse is greater in 31 Open-Bid Auctions First-Price Auctions Second-Price Auctions In second-price auctions the winner pays a price that is linked to other bidder s information which in fact mitigates winner s curse. Bidders revise downward their bids less.

32 Bidding Strategies 32 Auction English Dutch First-price sealed-bid Second-price sealed-bid Independent Private Values Bid up to willingness-to-pay Forecast others willingnesses-to-pay Forecast others willingnesses-to-pay Bid willingness-to-pay Correlated Values Observe others bids and adjust own willingness-to-pay Forecast others willingnessesto-pay and adjust own willingness-to-pay as price falls Forecast others willingnessesto-pay and adjust for winner s curse Adjust willingness-to-pay for winner s curse and bid willingness-to-pay

33 Comparing Auctions and Auction Design 33 W H I C H A U C T I O N D E S I G N S H O U L D A S E L L E R C H O O S E?

34 Auction Design Auctions are trading mechanism where rules are stated in advance. An auction designer (seller) is faced with choosing an auction type and so he must predict the behavior of bidders. Design issues: Simultaneous vs. sequential Sealed bid vs. open bid Single items vs. package bids Fully transparent vs. hide bidder identities Well designed auctions are efficient Winner s curse is minimized. Threat of collusion is mitigated. 34

35 Goals of Auction Design Maximize seller s expected revenue. 35 Maximize efficiency. Ensure the object(s) go to the bidders who value them the most. Serve other policy objectives. Promoting new entry and competition.

36 Expected Revenues with Private Values 36 Revenue Equivalence Theorem English Auction Secondprice sealedbid Firstprice sealedbid Dutch Auction NOTE English: Winner pays the 2 nd highest valuation. Second-price: Winner pays the 2 nd highest valuation. Dutch and First-price: Winner pays on average the 2nd highest valuation.

37 Expected Revenues with Correlated Values 37 English Auction Secondprice sealedbid Firstprice sealedbid Dutch Auction NOTE Optimal bidding requires to use information gained during the auction process. Winner s curse problem. English: A lot of information is revealed during the process. Winner s curse is mitigated which results in highest possible bids. Second-price: No new information. Strong winner s curse but winner pays 2 nd highest bid which mitigates (insures) the bidders risk and leads to higher bids than in Dutch or first-price auctions. Dutch and First-price: No new information. Strong winner s curse which implies very low bids.

38 Auction Design and Efficiency 38 English with no reserve price English with reserve price Dutch Sealed-Bid First-Price Sealed-Bid Second-Price Must be efficient. If a buyer with a low valuation was about to buy, the highest valuation buyer would bid higher. Need not be efficient. If the reserve price is set above the (unknown to the seller) highest buyer valuation, then there will be no sale and so no gains-to-trade. Need not be efficient. No buyer knows other buyers valuations, so the highest valuation buyer may delay too long and lose to another bidder Need not be efficient. No buyer knows other buyers valuations, so the highest valuation buyer may bid too low and lose to another bidder. Is efficient Even though no buyer knows the other buyers valuations, truth-telling ensures that the highest valuation bidder will win. Pareto efficiency: The item must be sold to the buyer with the highest valuation.

39 Auction Design: Pitfalls Winner s curse Bidders bids less than their true valuations. Affects sellers proceeds. Depends on the auction process. Threat of collusion (bid rigging) Bidders manipulate the auction result. Affects sellers proceeds. Can often be reduced. Bidder uncertainty Increases likelihood of inefficient or low-value assignments. Makes bidding difficult, undermines confidence, and can lead to defaults. Can often be reduced. 39

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41 Auctioneer 41 In a traditional auction, the auctioneer doesn't own the good, but acts rather as a mediator for someone who does. The auctioneer is not an agent or a participant in the exchange. Think of it as an automated set of rules. Manages communication and information exchange between participants. Provides structure and enforcement of rules.