Economics: Bidding Strategies & Auction Analysis

1. Economics 100C

2. Have you ever bid for anything on eBay? • Yes, frequently • Yes, but not frequently • No

3. Equilibrium bids in first and second price sealed bid auctions with private values. • Second price; bid true value. • First price; bid less than true value. • With uniform distributions if values and n bidders, equilibrium in first price auction has bidders bid fraction (n-1)/n of values.

4. Expected revenues with 2 bidders. • Second-price auction—Expected value of second highest bid. • First price auction---Expected value of half of highest bid. • If values are uniformly distributed on an interval [0,A], these both turn out to equal A/3. See posted notes.

5. Expected revenues with n bidders. • Second-price auction—Expected value of second highest bid. • First price auction---Expected value of half of highest bid. • If values are uniformly distributed on an interval [0,A], these both turn out to equal A(n-1)/(n+1). See notes.

6. An Oil Auction • This illustrates a “common value auction” in which different bidders have partial information about the value of object being auctioned. • Two bidders. Each has explored half of the oil field. • Whole oil field is up for bids.

7. Instructions: Classroom Experiment • Form groups of 3. Choose one person to be Auctioneer, one to be Player A and one to be Player B. • Players A and B not allowed to talk to each other. • Value of the oil field the sum of last two digits of A’s perm number and last two digits of B’s • Players A and B write their perm numbers and bids on slip of paper and pass them to auctioneer. • High bidder gets oilfield. Profits are value of oil field minus bid. Low bidder’s profits are zero. • Auctioneer records total value, bids and profits.

8. Is this oilfield auction a common value auction or a private values auction? • Common Value • Private Values

9. Answer • This is a common values auction. The oilfield is worth the same amount to whoever gets it. • The only difference between the bidders is that they have different bits of information. • This would be a private values auction if e.g. one firm could use the oilfield more effectively than the other.

10. In this auction, if you are Player A and your side of the oil field is worth 60, what is the expected value of the whole oil field? • 60 • 90 • 110 • 120 • 150

11. Expected Value or whole field if my side is worth 60 Value of other side is a random variable uniformly distributed on [0,100] Expected value of other side is 50. Expected total value is 60+50=110.

12. What happens if bidders bid expected values? • Each bidder would bid xi+50 where xi is the value of his own side. • Winner would be person with higher xi • Suppose that A wins and has value xA Given that he won, it must be that xB<xA • What is the expected value of xB conditional on xB<xA? • xA/2 • So expected value of oil field is xA/2+ xA= 3xA/2< xA+50. • On average, winning bidder would lose money.

13. The winner’s curse • In this auction, you would on average lose money if you bid as high as your expected value. • The expected value conditional on winning the auction is lower than the expected value. • This effect is called the winner’s curse.

14. Buying Montana • I will sell a contract in which I promise to pay $1 for every 100,000 people who live in Montana. • The sale will be by an English auction. • Top bidder pays me his bid. I pay top bidder $1 for every 100,000 people who live in West Montana.

15. Was there aWinners Curse? • If so, why?

16. See you Thursday Don’t forget your clicker.