Auctions

1. Auctions Ruth Tarrant

2. Classifying auctions What is the nature of the good being auctioned? What are the rules of bidding? Common value auction Private value auction English, Dutch, sealed-bid or Vickrey? Each bidder has a potentially different valuation of the good owing to tastes and preferences e.g. fine art The good has the same value to each bidder but they may have different estimates of that value e.g. off-shore drilling rights

3. Rules of bidding – private value auctions (1) • English auction (most common) • Start with a ‘reserve price’ (the lowest that the seller will accept) • Bidders offer successively higher prices • When no bidder is prepared to go higher the good is awarded to the highest bidder • Dutch auction • Auctioneer starts with a high price and lowers it step by step until someone is prepared to buy it • Very rapid!

4. Rules of bidding – private value auctions (2) • Sealed-bid auction • Each bidder writes their bid on paper and seals it in an envelope, which are collected and opened, and the good is awarded to the highest bidder (or possibly lowest bidder depending on auction) • Common for construction work and large projects where the job will be awarded to the lowest bid • Vickrey auction • Like sealed bid but the good is awarded to the highest bidder but at the second highest price

5. How do we choose the type of auction? (1) Two goals Pareto efficiency Profit maximisation The good must be assigned to the person with the highest value The good must be assigned to the person with the highest value (Alice values it higher than Bob – if Bob receives it then you can make both better off by Alice transferring the good to Bob and Bob paying Alice some value between Alice’s value and Bob’s value)

6. How do we choose the type of auction? (2) • English auction • Pareto efficiency: yes! • Profit maximisation: difficult to say because the winning bidder may have gone higher if he had been pushed by other bidders • Susceptible to collusion

7. How do we choose the type of auction? (2) • Dutch auction • Pareto efficiency: no guarantee that the good will go to the person with the highest valuation as they may wait too long to bid • The optimal bid depends on the highest bidder’s beliefs about the values of other bidders

8. How do we choose the type of auction? (3) • Sealed-bid auction • Similar to Dutch auction as the optimal bids by each bidder depends on their beliefs about the bids of others, so can’t guarantee Pareto efficiency or profit maximisation

9. How do we choose the type of auction? (4) • Vickrey auction • If everyone bids their ‘true’ value the bidder with the highest valuation will receive the good (same as the English auction) • We can prove mathematically that bidders have an incentive to bid truthfully in this type of auction, so it’s the quickest and most likely to achieve Pareto efficiency and profit maximisation as a result

10. The Winner’s Curse – common value auctions • Assume that the rights or goods are given to the highest bidder • The winner will win only by being overly optimistic!

11. Questions • Is an auction of antique quilts to collectors a private-value or common-value auction? • Suppose there are 2 bidders with values of £8 and £10 for the item, with a bid increment of £1. What is the profit maximising reservation price for an English auction? • A teacher fills a jar with pennies and auctions it off using an English auction. Is this a private-value or common-value auction? Will the winning bidder usually make a profit?

12. Questions 4. Suppose there are 2 bidders for an item. The seller believes the bidders have a value of £10 or £100. Assume these two cases are equally likely: • What is the expected revenue to the seller? • Is there any way the seller can do better than this?

13. Questions 5. A dealer decides to sell an antique car by means of an English auction with a reservation price of £900. There are 2 bidders. The dealer believes that there are only 3 possible values that each bidder’s valuation might take: £6300, £2700 and £900, each with equal probability. Assuming that the bidders bid rationally and don’t collude, what is the dealer’s expected revenue from selling the car?

14. Questions 6. A bank repossesses a house and sells it off at auction. There are 3 bidders. The bank believes that each of the bidders has a probability of 1/3 of valuing the house at £700,000, a probability of 1/3 of valuing it at £500,000 and a 1/3 probability of a £200,00 valuation. These probabilities are independent between buyers. If the bank uses a Vickrey auction, what will the bank’s expected revenue be from the sale?