The Privacy Cost of the Second Chance Offer

Joshi, Sun, Vora

Sumit Joshi, Yu-An Sun, Poorvi VoraThe George Washington University

The Privacy Cost of the Second Chance Offer

The Privacy Cost of the Second Chance Offer, WPES ‘05

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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 : k+1 independent auctions

• First object sells at x2

• ith object at xi+1

• ith highest bidder has payoff xi – xi+1


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Case : Example k=2

↑

Price

Number of buyers →1 2 3

Revenue: Case

Bidder Payoff


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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 k=2

↑

Price


Revenue: Case A


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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


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Case B, Rational Bidder. Example k=2

↑

Price


Revenue Loss: Case B; Bidder Payoff

Revenue: Case B


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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


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Case C, Anonymity. Example k=3

↑

Price


Revenue Loss: Case C; Bidder Payoff

Revenue: Case C

Revenue Loss: Case C; Opportunity LossCase B price


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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

Revenue

Expected Number of Buyers

Price


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eBay Auction of Annexation Drone

Bid Order eBay Identity Bid Value non-strategic

b1 erelfir 13.50

b2 les-letwin 13.00

b3 daredevilgo 5.55

b4 jan1923 5.09


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Bid Order eBay Identity Bid Value Price Non-strategic

b1 erelfir 13.50 13.50

b2 les-letwin 13.00 13.00

b3 daredevilgo 5.55 5.55

b4 jan1923 5.09 -


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Price

Strategic

b1 erelfir 13.50 13.50 5.12

b2 les-letwin 13.00 13.00 5.11

b3 daredevilgo 5.55 5.55 5.10

b4 jan1923 5.09 - -


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Price

Strategic

Price

Auctions

b1 erelfir 13.50 13.50 5.10 13.50

b2 les-letwin 13.00 13.00 5.10 5.56

b3 daredevilgo 5.55 5.55 5.10 5.10

b4 jan1923 5.09 - -


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Payoff and Revenue Relationships

RA

RBRD

RRC

A

DB

C


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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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RA

RBRD

RRC

A

DB

C


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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.


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RA

RBRD

RRC

A

DB

C


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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 k=1, 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

Date post:	05-Jan-2016
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The Privacy Cost of the Second Chance Offer

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