The Privacy Cost of the Second Chance Offer

1. The Privacy Cost of the Second Chance Offer Sumit Joshi, Yu-An Sun, Poorvi Vora The George Washington University

2. Our Privacy Model • The privacy problem is one of information revelation in a multi-stage game • Example multi-stage game: a series of online auctions and fixed-price sales • Current move reveals information about future moves. • When this results in economic disadvantage to the player, the current move bears a privacy cost The Privacy Cost of the Second Chance Offer, WPES ‘05

3. Example Game: Auction • A losing bidder in an auction typically reveals her valuation – the highest she is willing to pay • This can be used later to: • Provide her information on other interesting sales, if she is considered a serious buyer • Charge her a higher price than others because her valuation is high The Privacy Cost of the Second Chance Offer, WPES ‘05

4. Privacy Cost can be Reduced Through • Cryptography • Protect bidder identity, but reveal bid • Reveal neither bid nor bidder • Rational agents • Bid on behalf of bidder, optimizing overall multi-stage payoff (i.e. predict and minimize privacy cost) The Privacy Cost of the Second Chance Offer, WPES ‘05

5. Second-Chance Offer • Stage I: Normal, ascending-bid open-cry auction • Stage II: Take-it-or-Leave-it Offer to k losing bidders at highest bid • Considerable evidence implies bidders do not behave strategically and bid as though no Stage II The Privacy Cost of the Second Chance Offer, WPES ‘05

6. Stage I: A regular eBay auction In a regular English auction, bidder withdraws when Bid = x • where x is the valuation The sale price is the second-highest valuation: x2 because winner need not raise bid higher The payoff to the winner is the difference between the first and second-highest valuations x1 – x2 ≥ 0 The Privacy Cost of the Second Chance Offer, WPES ‘05

7. Stage II: Take It Or Leave It If a bidder who loses in Stage I has bid as in a normal English auction, the seller knows his valuation, and charges him that value Payoff to winner of Stage I is x1 – x2 ≥ 0 Payoff to all other bidders in Stage II: xi – xi = 0 The Privacy Cost of the Second Chance Offer, WPES ‘05

8. This paper studies Effect of using information across stages: • Only seller: • Case A: Non-strategic Bidders • Both seller and bidders: • Case B: Strategic Bidders The Privacy Cost of the Second Chance Offer, WPES ‘05

9. This paper also studies (Cryptographic) Bidder Protection when seller uses information across stages but bidder does not: • Case C: Non-strategic Bidders + Anonymity • Case D: Non-strategic Bidders + Anonymity + Bid Secrecy The Privacy Cost of the Second Chance Offer, WPES ‘05

10. And compares to Neither party uses information across stages: • Case : k+1 independent auctions • First object sells at x2 • ith object at xi+1 • ith highest bidder has payoff xi – xi+1 The Privacy Cost of the Second Chance Offer, WPES ‘05

11. Case : Example k=2 Bidder Payoff ↑ Price Revenue: Case  3 2 1 Number of buyers → The Privacy Cost of the Second Chance Offer, WPES ‘05

12. Case A: Non-strategic Bidder • Bidder payoff lowest possible. Zero except for highest bidder • Seller revenue highest possible The Privacy Cost of the Second Chance Offer, WPES ‘05

13. Case A: Example k=2 ↑ Price Revenue: Case A 3 2 1 Number of buyers → The Privacy Cost of the Second Chance Offer, WPES ‘05

14. Case B: Strategic BidderPrice Discrimination Certain • Two can play a game: top k bidders do not bid higher than k+1th highest bid • Revenue lower, payoff higher, than in consecutive auctions The Privacy Cost of the Second Chance Offer, WPES ‘05

15. Case B, Rational Bidder. Example k=2 Revenue Loss: Case B; Bidder Payoff ↑ Price Revenue: Case B 3 2 1 Number of buyers → The Privacy Cost of the Second Chance Offer, WPES ‘05

16. Case C:Non-Rational Bidder + Anonymity • Bids are known, but not corresponding bidders • Seller estimates a single price that will provide largest revenue • This price not smaller than that of Case B • Payoff and revenue between those of Case A and Case B The Privacy Cost of the Second Chance Offer, WPES ‘05

17. Case C, Anonymity. Example k=3 Revenue Loss: Case C; Bidder Payoff ↑ Price Revenue: Case C Case B price Revenue Loss: Case C; Opportunity Loss 3 2 1 Number of buyers → The Privacy Cost of the Second Chance Offer, WPES ‘05

18. Case D: Anonymity + Bid Secrecy • Seller uses highest bid and probability distribution to estimate price for maximum revenue • This revenue strictly smaller than Case C because seller has less information • Payoff may be smaller or larger The Privacy Cost of the Second Chance Offer, WPES ‘05

19. Case D: Expected Revenue Revenue Loss, Bidder Payoff Expected Number of Buyers Revenue Price The Privacy Cost of the Second Chance Offer, WPES ‘05

20. eBay Auction of Annexation Drone The Privacy Cost of the Second Chance Offer, WPES ‘05

21. eBay Auction of Annexation Drone The Privacy Cost of the Second Chance Offer, WPES ‘05

22. eBay Auction of Annexation Drone The Privacy Cost of the Second Chance Offer, WPES ‘05

23. eBay Auction of Annexation Drone The Privacy Cost of the Second Chance Offer, WPES ‘05

24. Payoff and Revenue Relationships RA A RC R C  RB B D RD The Privacy Cost of the Second Chance Offer, WPES ‘05

25. Main Results: Two can play a game Price discrimination with a rational bidder is a disadvantage to the seller when compared to consecutive auctions That is, if both parties are allowed to use information across stages, the seller loses The Privacy Cost of the Second Chance Offer, WPES ‘05

26. Payoff and Revenue Relationships RA A RC R C  RB B D RD The Privacy Cost of the Second Chance Offer, WPES ‘05

27. Main Results:Protection creates Opportunity Loss Provision of anonymity decreases revenue. Further provision of bid secrecy further reduces it. But this does not always create a corresponding payoff increase, because of potential opportunity loss. The Privacy Cost of the Second Chance Offer, WPES ‘05

28. Payoff and Revenue Relationships RA A RC R C  RB B D RD The Privacy Cost of the Second Chance Offer, WPES ‘05

29. Main Results: Rationality better than Anonymity/Bid Secrecy Rationality provides higher payoff and lower revenue than anonymity. Rationality provides higher payoff than Case A even when k=1, though anonymity and bid secrecy do not (sale price reveals second highest valuation). The Privacy Cost of the Second Chance Offer, WPES ‘05

30. Main Results: Anonymity and Bid Secrecy Do Not Provide a Level Playing Field Privacy protection does not always provide the bidder an advantage over consecutive auctions. The Privacy Cost of the Second Chance Offer, WPES ‘05

31. Main Results: Privacy is a concern of the rich Privacy protection and rationality provide more advantage to higher valuations Opportunity Loss is more frequent for lower valuations The Privacy Cost of the Second Chance Offer, WPES ‘05

32. Further Directions • What if seller strategy random and can be learnt by bidder? • What if seller uses bid to determine price for related goods? • More general model for general multi-stage game The Privacy Cost of the Second Chance Offer, WPES ‘05