Ch17Auctions(中级微观经济学-清华大学-钟笑寒).ppt

1、Chapter Seventeen,Auctions,Market Mechanisms,In our equilibrium analysis, we simply assume a competitive market: Each agent is a price-taker. Prices adjust until demand equals supply equilibrium price and quantity. Pareto Efficiency is achieved then. But how is this hypothetic market relevant to rea

2、l-world market mechanisms?,Market Mechanisms,Economists study market mechanisms basically through two approaches. Theoretically, we study some well-defined market mechanisms esp. auctions, to give us some ideas on general market mechanisms. Empirically, we test competitive market hypothesis through

3、some well-designed experimental market mechanisms.,Market Mechanisms,Vernon Smith (the 2002 Nobel laureate) once set up an experiment in a so-called double oral auction, a market mechanisms used in many financial and commodity markets. Subjects were randomly assigned the roles of seller and buyer. E

4、ach seller was given one unit of the good to be sold, and a reservation price v for this unit, which is her own private information. Each buyer was also assigned a private reservation price w.,Market Mechanisms,Smith concluded that “ there are strong tendencies for a competitive equilibrium to be at

5、tained as long as one is able to prohibit collusion and to maintain absolute publicity of all bids, offers, and transactions. Changes in the conditions of supply and demand cause changes in the volume of transaction per period and the general level of contract prices. These latter correspond reasona

6、bly well the predictions of competitive price theory.”,Why Study Auctions?,By proceeding from simpler to more complex auction forms, theory has deepened our understanding of the functioning of many real-world markets. Even some of the simpler auction forms studied in theory are widely used in practi

7、ce, particularly in the context of deregulation and privatization of natural monopolies, public procurement, the sale of government bonds, etc.,Who Uses Auctions?,Owners of art, cars, stamps, machines, mineral rights etc. Q: Why auction?,Who Uses Auctions?,Owners of art, cars, stamps, machines, mine

8、ral rights etc. Q: Why auction? A: Because many markets are imperfect and it is hard to discover potential buyers true valuations of your asset. Auctions help to discover this information.,Types of Auctions,English auction: bids are public announcements bid price rises until there are no further bid

9、s highest bid wins winner pays his bid.,Types of Auctions,Sealed-bid first-price auction: bids are private information bids are made simultaneously highest bid wins winner pays his bid.,Types of Auctions,Sealed-bid second-price auction: bids are private information bids are made simultaneously highe

10、st bidder wins winner pays second-highest bid also known as a Vickrey auction.,Types of Auctions,Dutch auction: auctioneer announces a high bid and then gradually lowers the bid first buyer to accept wins and pays that price.,Reserve Price,A seller specified bid level below which no sale is made.,Ec

11、onomists Classification of Auctions,Private-value auctions: every potential buyer knows for sure her own valuation of the item for sale all these individual valuations are independent of each other.,Economists Classification of Auctions,Common-value auctions: item for sale has the same value to ever

12、y potential buyer potential buyers differ in their own estimates of this common value.,Auction Design,Goals: Pareto efficiency maximization of the sellers profit.,Auction Design,Pareto efficiency: the item must sell to the buyer with the highest valuation of the item. Which auctions are Pareto effic

13、ient?,Auctions and Efficiency,English auction with no reserve price must be efficient since, if a buyer with a low valuation was about to buy, the highest valuation buyer would bid higher.,Auctions and Efficiency,English auction with a reserve price need not be efficient since if the reserve price i

14、s set above the (unknown to the seller) highest buyer valuation, then there will be no sale and so no gains-to-trade.,Auctions and Efficiency,Dutch auction need not be efficient. No buyer knows other buyers valuations, so the highest valuation buyer may delay too long and lose to another bidder.,Auc

15、tions and Efficiency,Sealed-bid first-price auction need not be efficient. No buyer knows other buyers valuations, so the highest valuation buyer may bid too low and lose to another bidder.,Auctions and Efficiency,Sealed-bid second-price auction is Pareto efficient even though no buyer knows the oth

16、er buyers valuations (more on this later).,Why Use a Reserve Price?,Suppose there are 2 buyers. The seller believes each buyers valuation is $20 with chance 1/2 and $50 with chance 1/2.,Why Use a Reserve Price?,I.e. with chance 1/4 each, the seller believes she faces buyer valuations ($20,$20), ($20

17、,$50), ($50,$20) and ($50,$50). Use an English auction. Bids must be raised by at least $1.,Why Use a Reserve Price?,With chance 1/4 each, winning bids will be $20, $21, $21 and $50 if there is no reserve price. Sellers expected revenue is($20 + $21 + $21 + $50)/4 = $28with no reserve price.,Why Use

18、 a Reserve Price?,Set a reserve price of $50. With chance 1/4 there will be no sale. With chance 3/4 the winning bid will be $50.,Why Use a Reserve Price?,Set a reserve price of $50. With chance 1/4 there will be no sale. With chance 3/4 the winning bid will be $50. Sellers expected revenue is,Reser

19、ve Price and Efficiency,The reserve price causes an efficiency loss since, with chance 1/4, there is no trade.,Second-Price, Sealed-Bid Auction,bids are private information bids are made simultaneously highest bidder wins winner pays second-highest bid also known as a Vickrey auction.,Second-Price,

20、Sealed-Bid Auction,No bidder knows any other bidders true valuation of the item for sale. Yet, it is individually rational for each bidder to state truthfully his own valuation. Why? E.g. two bidders with true valuations v1 and v2.,Second-Price, Sealed-Bid Auction,E.g. two bidders with true valuatio

21、ns v1 and v2. Bids are b1 and b2. Expected gain to bidder 1 is,Second-Price, Sealed-Bid Auction,Expected gain to bidder 1 is How is this maximized? If v1 b2, then maximize the prob. of winning; i.e. set b1 = v1. If v1 b2, then minimize the prob. of winning; i.e. set b1 = v1. Either way, telling the

22、truth is best!,Second-Price, Sealed-Bid Auction,Since truth-telling is best for every bidder, the highest valuation bidder will win. Hence the second-price, sealed-bid auction is Pareto-efficient.,Common-Value Auctions,The item for sale has the same value to every potential buyer. Potential buyers d

23、iffer in their own estimates of this common value. Bidder is estimate iswhere is the common value and is bidder is estimation error.,Common-Value Auctions,Bidder is estimate iswhere is the common value and is bidder is estimation error. If every bid is truthful, the winner is the bidder with the lar

24、gest estimation error so a truthful winner on average pays more than the true value - the winners curse.,Common-Value Auctions,If every bid is truthful, the winner is the bidder with the largest estimation error - call it If then a truthful winner on average pays more than the true value - the winners curse. So bids should on average be less than in a common-value aucti