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Chapter 25: Auctions and Auction Markets 1 Auctions and Auction Markets

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Chapter 25: Auctions and Auction Markets 2 Introduction Auctions have an old history and are increasingly common –193 AD, Praetorian Guard auctioned off the the Roman Empire to Marcus Didius Salvius Julianus –Modern Examples eBay (Consumers) Covisint/Free Markets (B2B) Wireless Spectrum Auction (Government2B)

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Chapter 25: Auctions and Auction Markets 3 Auction Types Ascending Bid or English Auction –Probably most familiar—Price starts low –Price is raised gradually until only one bidder remain Descending Bid or Dutch –Price starts high –Price is lowered until someone finally wants to buy Sealed Bid Auctions –Bids effectively submitted in sealed envelopes First-Price Sealed Bid: Winning bidder pays amount bid Second-Price Sealed Bid: Winning bidder pays amount equal to second-highest bid Private Value Auction—Item value different for each bidder Common Value Auction—Item value common to all bidders but each has different information about true common value

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Chapter 25: Auctions and Auction Markets 4 The Revenue Equivalence Theorem Revenue to Seller is Same Regardless of Auction Type in a Private Value Auction Consider auction of textbook among 170 students Values start at $0.50 and increase by $0.50 with each student. So, top value is $85 –Consider English Auction where Auctioneer raises price by 1¢ each round When bid reaches $84.50, only two bidders remain Final winning bid will be $84.51 when only one bidder is left –Second Price Sealed Bid If bidders bid their true values, top two bidders will bid $85 and $84.50, respectively Bidder with $85 valuation will win but pays only $84.50 $84.51

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Chapter 25: Auctions and Auction Markets 5 Revenue Equivalence (Cont.) Why bid one’s true value in Second-price, sealed bid auction? –What one bids determines only if one wins—not what one pays Bidding less than true value risks losing the object to someone who values it less than one is willing to pay without changing the price Bidding more than true value raises chance of winning but only by beating out a bidder with a higher value than your own You will then pay that higher value and, since it exceeds your own, lose out

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Chapter 25: Auctions and Auction Markets 6 Revenue Equivalence (Cont.) Winning Bid in a First-Price, sealed bid auction –bidders observe no other information about other bidder’s value prior to making a bid –Winner pays the winning bid –Suggested Strategy: Bid an amount equal to one’s best guess of next highest bid Treat your value as the highest (if it’s not, winning is too costly) If valuations are uniform, next highest is (N –1)/N of your value E.g., bidder with value $85, bids (N –1)/N *$85 = $84.50, N = 170 –Here again, winning bid is $84.50 –This is a general result and important. We don’t want an object’s value to depend on how it was bought

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Chapter 25: Auctions and Auction Markets 7 Revenue Equivalence (Cont.) Dutch or descending price auction is strategically identical to first-price, sealed bid auction. Again, in both: –bidders observe no other information about other bidder’s value prior to making a bid –Winner pays the winning bid –Optimal strategy should be the same in both –So, winning bid will again be $84.50 Revenue Equivalence: Regardless of auction type, the winning bid or payment is always $84.50 – This is a quite general result. In private value auctions, the revenue to the seller is the same regardless of what type of auction is held –It is good that Revenue Equivalence holds. We do not want an object’s price to depend on how it is bought

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Chapter 25: Auctions and Auction Markets 8 Common Value Auctions In common value auctions, item has an unknown but common market value, e.g., real estate Bidders have different information about the true value That true value depends on what others are willing to pay Revenue Equivalence may not hold The “Winner’s Curse” in Common Value Auctions Winner of a common value auction is one with highest estimate of true common value, e.g., highest estimate of the value of a property Winning can be bad news. It reveals that the winner’s information was most upward biased and bid was higher than the average or expectation of the true value

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Chapter 25: Auctions and Auction Markets 9 Common Value Auctions (cont.) Minimizing the Winner’s Curse –To avoid the winner’s curse, bidders need to shade their bids below that indicated by their information –This requires recognizing that one is interested in the object’s true value if one wins the bid, i.e., if one wins, that says something about the object’s true value –Need somehow to use this information to estimate the average or expected mean value of the property Again, assume that your estimate E is the highest (you’re not interested in the object’s value if it is not) If there are N bidders and the distribution is uniform, then highest value of E is on average, U(N-1)/N where U is the upper limit of the distribution. Solving for U yields: U = [N/(N-1)]E Average Estimate is [N/2(N-1)]E. This is the amount to bid. It is well below E which is why it helps one minimize the winner’s curse.

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Chapter 25: Auctions and Auction Markets 10 Common Value Auctions (cont.) For example, if there are 100 bidders each drawing estimates of a property’s value such that those estimates are uniformly distributed; and if my estimate is $10,000 –My best guess is that the uniform distribution ranges from 0 to [100/(100-1)]$10,000 or from 0 to $10,101 –My guess for the average value of the estimates is therefore $5,050.50 –I bid much less than the estimated property value in an effort to avoid the winner’s curse of paying too much With Common Value auctions, all auction types may not generate the same revenue— Ascending price auctions, for example, reveal more information than other types about the estimates of other bidders—Revenue Equivalence can break down

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Chapter 25: Auctions and Auction Markets 11 Almost Common Value Auctions Some auctions are a mix of private and common valuations –“Almost common value auctions” are those in which the object has a common value to nearly all bidders but one who values the object by some amount, v, above everyone else –Surprisingly, even when v is small, the effect on revenue can be large. Why? Because the winner’s curse cuts doubly in this setting Example: 5 local coffee shops and Starbuck’s all bid for a coffee store Whatever the store is worth to the locals, it’s worth more to Starbuck’s As a result, each local bidder faces an intensified winner’s curse To win the bid, it must beat Starbuck’s bid which is biased upwards This means that its estimate must really be unusually high Accordingly, local bidders shade their bids even more But this allows Starbuck’s to be more aggressive, causing locals to shade their bids even more Starbuck’s will win the bidding but at a much reduced price

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Chapter 25: Auctions and Auction Markets 12 Auction Markets and Industrial Organization Auction markets are affected by the problems of monopoly and collusion that affect other markets Auction design can be helpful in this regard –Ascending auction can limit winner’s curse effects but: Facilitates collusion Facilitates communication of asymmetric values –On both counts, the English auction may result in lower revenue Sealed bid designs works well –It encourages entry because there is a chance of winning even if a firm’s estimated value is not the highest –It reduces collusion opportunities However, there can be too many bidders. Winner’s Curse rises with the number of bidders. The price-raising effect of more bidders may be offset by the price-shading effect.

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