Sumit Joshi, YuAn Sun, Poorvi Vora

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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

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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

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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)

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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

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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

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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

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This paper studies

• Effect of using information across stages
• Only seller
• Case A Non-strategic Bidders
• Both seller and bidders
• Case B Strategic Bidders

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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

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And compares to

• Neither party uses information across stages
• Case ? k1 independent auctions
• First object sells at x2
• ith object at xi1
• ith highest bidder has payoff xi xi1

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Case ? Example k2
Bidder Payoff
? Price
Revenue Case ?
2
3
1
Number of buyers ?
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Case A Non-strategic Bidder

• Bidder payoff lowest possible. Zero except for
  highest bidder
• Seller revenue highest possible

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Case A Example k2
? Price
Revenue Case A
2
3
1
Number of buyers ?
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Case B Strategic BidderPrice Discrimination
Certain

• Two can play a game top k bidders do not bid
  higher than k1th highest bid
• Revenue lower, payoff higher, than in consecutive
  auctions

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Case B, Rational Bidder. Example k2
Revenue Loss Case B Bidder Payoff
? Price
Revenue Case B
2
3
1
Number of buyers ?
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Case CNon-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

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Case C, Anonymity. Example k3
Revenue Loss Case C Bidder Payoff
? Price
Revenue Case C
Case B price
Revenue Loss Case C Opportunity Loss
2
3
1
Number of buyers ?
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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

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Case D Expected Revenue
Revenue Loss, Bidder Payoff
Expected Number of Buyers
Revenue
Price
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eBay Auction of Annexation Drone
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eBay Auction of Annexation Drone
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eBay Auction of Annexation Drone
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eBay Auction of Annexation Drone
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Payoff and Revenue Relationships
RA
?A
R?
RC
??
?C
RB
?D
?B
RD
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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

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Payoff and Revenue Relationships
RA
?A
R?
RC
??
?C
RB
?D
?B
RD
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Main ResultsProtection 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.

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Payoff and Revenue Relationships
RA
?A
R?
RC
??
?C
RB
?D
?B
RD
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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 k1, though anonymity and bid secrecy
  do not (sale price reveals second highest
  valuation).

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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.

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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

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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