1. week 51 COS 444 Internet Auctions: Theory and Practice Spring 2010 Ken Steiglitz ken@cs.princeton.edu

2. week 52

3. 3 Field Experiment “ Public Versus Secret Reserve Prices in eBay Auctions: Results from a Pokémon Field Experiment,” R. Katkar & D. Lucking-Reiley, 1 December 5, 2000. “We find that secret reserve prices make us worse off as sellers, by reducing the probability of the auction resulting in a sale, deterring serious bidders from entering the auction, and lowering the expected transaction price of the auction. We also present evidence that some sellers choose to use secret reserve prices for reasons other than increasing their expected auction prices.”

4. week 54 Pros and cons of secret reserve Pros: By comparison with equal open reserve, attracts bidding activity, which is generally good because 1) more bidding attracts more bidders, 2) bidders fear “winner’s curse” less with more revealed information (more later, Milgrom & Weber 82), and so bid higher Cons: Sends signal that price will be high, discourages entry Extra fee on eBay

5. week 55 Field Experiment… Katkar & L-R 00 50 matched pairs of Pokémon cards 30% book value, open & secret reserve Open reserve increased prob. sale: 72% vs. 52% Open reserve yielded 8.5% more revenue Caution: these are low-priced items! Caution: is it reasonable to match equal secret and open reserves? Is this the right question? Use low opening? Risk on high-value items ? Evidence of illicit transactions around eBay

6. week 56 Field Experiment… Katkar & L-R 00 Notice that they “… concluded with a notice that we intended to use data on bids for academic research, and provided contact information for questions or concerns.” Do you think this affected results?

7. week 57 All-Pay auction Here’s a different kind of auction: High bidder wins the item All bidders pay their bids! … the All-Pay Auction Models political campaigning, lobbying, bribery, evolution of offensive weapons like antlers,… etc. What’s your intuiton? How do you bid? Is this better or worse for the seller than first-price? Second-price?

8. week 58 All-pay equilibrium Start with your value = v E[surplus] = pr{1 wins} [ v ] – b ( v ) pay in any event In value space, “bid as if your value = z” E[surplus] = vF(z) n-1 – b(z) And set derivative to zero at z=v.

9. week 59 All-pay equilbrium, con’t Differentiating and setting z=v: Integrating and using b(0)=0: Uniform-v case: Note: once again, b ΄ > 0, verifying monotonicity.

10. week 510 Expected rev. for uniform v’s of all-pay = FP = SP In all-pay auction, E[pay] = bid Averaging over v for each bidder: Times n bidders: Same as SP, FP! More revenue equiv.!

11. week 511 Related to all-pay: War of Attrition Suppose two animals are willing to fight for a time (b 1, b 2 ). One gives up, the other wins. The price paid by the winner is min (b 1, b 2 ). Essentially a second-price all-pay: the winner pays second-highest bid, losers pay their bids.

12. week 512 Rev. equiv. FP=SP for general distributions In SP auctions, expected revenue = expected price paid = expected value of second-highest bid in equil. In equil. means truthful bidding in SP auctions, of course.

13. week 513 Rev. equiv. FP=SP for general distributions In FP auctions, expected revenue = n E [payment of bidder 1 in equil.] = n E [b fp (v 1 ) pr{1 wins} ] Now just plug in the known equil. bidding function:

14. week 514 Rev. equiv. FP=SP for general distributions … and use integration by parts mercilessly, yielding

15. week 515 Notice that this is also the revenue for general distributions in the all-pay auction

16. week 516 Back to eBay: timing of bids Pro sniping (strategic): Avoids bidding wars Avoids revealing expert information (if you are an expert) [Roth & Ockenfels 02, Wilcox 00]Roth & Ockenfels 02 Avoids being shadowed (possible?) Possibly conceals your interest entirely [Ockenfels & Roth 06] suggest implicit collusion (a weak version of the prisoner’s dilemma)Ockenfels & Roth 06

17. week 517 [Roth & Ockenfels 02, Wilcox 00] Evidence from the field Roth & Ockenfels: Computers vs. antiques Wilcox: Power drills, etc. vs. pottery Bidding on collectibles later than bidding on commodities eBay bidding later than on Amazon (where deadline is extensible) Bidders with high feedback later than those with low feedback on eBay

18. week 518 [Ockenfels & Roth 06] Argument pro sniping Suppose there is a significant chance of a snipe missing the deadline Then sniping can amount to “implicit collusion”, similar to an iterated prisoner’s dilemma  Depends on assumption of unreliable sniping (?, see eSnipe, eg)

19. week 519 [Ockenfels & Roth 06] Argument pro sniping Suppose two bidders, each misses deadline with prob. ½ Each decides to bid truthfully Each decides to bid exactly once, either early or late (snipe) Each has private value = $21 Starting bid = $1

20. week 520 [Ockenfels & Roth 06] Argument pro sniping Game matrix, expected payoffs Defect  Cooperate 

21. week 521 [Ockenfels & Roth 06] Argument pro sniping Game matrix, expected payoffs An iterated Prisoner’s Dilemma! Actually, “Friend or Foe” game show because 0/0 is a weak equilibrium See Axelrod, Evolution Of Cooperation, Basic Books, NY, 1984

22. week 522 Back to eBay: timing of bids Pro sniping (nonstrategic): Delays commitment Or just procrastination Soon-to-expire may be displayed first in search Willingness to pay increases with time --- “endowment effect” [Knetsch & Sniden 84, Kahneman, Knetsch, Thaler 90, Thaler 94]

23. week 523 Back to eBay: timing of bids Anti sniping (strategic early bidding): Scares away competition Raising one’s own bid even scarier [Rasmusen 06] suggests cost of discovery leads to a collusive equilibriumRasmusen 06

24. week 524 [Rasmusen 06] Argument pro early bidding Bidder 1 is uncertain of her value, can pay cost c to discover; bidder 2 is certain of his value 1 starts with low bid 2 bids early to signal if his value is high 1 pays to discover her value on signal With carefully chosen c this is mutually beneficial --- an asymmetric equilibrium Do you believe this?

25. week 525 Back to eBay: timing of bids Anti sniping (nonstrategic early bidding): Allows you to sleep, eat, etc. (But sniping services and software solve this problem.) Psychological reward for being listed as high bidder Sniping may be perceived as underhanded, cowardly, unethical