ebay auctions - the effect of bid increments and proxy bidding
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04/10/23
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The Effects of Proxy Bidding and Minimum Bid Increments
within eBay Auctions
Alex Rogers, Esther David & Nicholas R. JenningsUniversity of Southampton, UK.
Jeremy Schiff
Bar-Ilan University, Israel.
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Contents
• Introduction– eBay auctions
• eBay Auction Revenue– Proxy bidding– Pedestrian bidding
• eBay Bid History– Number of observed bids– Bid timing
• Bidding Strategies– Sniping
• Conclusions
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Contents
• Introduction– eBay auctions
• eBay Auction Revenue– Proxy bidding– Pedestrian bidding
• eBay Bid History– Number of observed bids– Bid timing
• Bidding Strategies– Sniping
• Conclusions
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eBay Auctions
• Most common online auction:– 1.9 billions items listed & $44.2 billion gross
merchandise sales in 2005.
• eBay trivia– Largest item sold – WWII submarine.– Largest item listed – WWII aircraft carrier.– Most expensive item sold
– Gulfstream jet ($4.9 million)
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eBay Auctions
• Unique properties:– Fixed deadline.– Proxy bidding system.– Minimum bid increment.
• Why study it?– Practical protocol for real world problems?– ‘It’s like a second price auction but the revenue is the
second highest price plus the minimum bid increment.’
– ‘Bidding as late as possible is the best strategy.’
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eBay Auctions Rules
• Seller set auction duration and starting bid.• Bidders enter maximum amount they are
prepared to bid to a proxy bidding system.• First bid must exceed the starting bid.• Subsequent bids must exceed the current
auction price by a minimum bid increment.• The bidder who entered the highest bid wins but
pays minimum of highest bid and second highest bid plus minimum bid increment.
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Example
Bidder Bid Auction Price Winner
A $3.50 $1.99 A
Starting bid: $1.99 Minimum bid increment: $0.25
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Example
Bidder Bid Auction Price Winner
A $3.50 $1.99 A
B $3.40 $3.50 A
Starting bid: $1.99 Minimum bid increment: $0.25
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Example
Bidder Bid Auction Price Winner
A $3.50 $1.99 A
B $3.40 $3.50 A
C $3.60
Starting bid: $1.99 Minimum bid increment: $0.25
Bid Not Accepted!
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Example
Bidder Bid Auction Price Winner
A $3.50 $1.99 A
B $3.40 $3.50 A
C $3.60
D $4.00 $3.75 D
Starting bid: $1.99 Minimum bid increment: $0.25
If D bids first, closing price could be $3.65, $3.75 or $3.85 depending on the bidding order.
Bid Not Accepted!
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eBay Auctions Rules
• eBay auctions are inefficient – the bidder with the highest valuation doesn’t always win.
• The revenue depends on the order that bidders arrive and the minimum bid increment.
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Contents
• Introduction– eBay auctions
• eBay Auction Revenue– Proxy bidding– Pedestrian bidding
• eBay Bid History– Number of observed bids– Bid timing
• Bidding Strategies– Sniping
• Conclusions
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eBay Auction Revenue
• Initially consider 2 bidders.
– eBay proxy bidding
Enter valuation as the maximum amount prepared to bid.
Not dominant strategy but we want to understand the protocol. eBay auctions aren’t in equilibrium.
– Pedestrian biddingIncrease the bid by the minimum bid increment whenever outbid.
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eBay Proxy Bidding
• First bidder bids v1.
• Closing price depends on v2 and d.
• Integrate over probabilities and revenues.
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Pedestrian Bidding
• Auction price increments in steps of d.• Equivalent to an English auction with discrete
bid levels.
• m bid levels with value li.
where
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Revenue Comparison
eBay Proxy Bidding
Pedestrian Bidding
Uniform bidders’ valuation distribution [0,1]
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Revenue Comparison
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More Than Two Bidders
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Optimal Bid Increment
Uniform [0,1]
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Optimal Bid Increment
Normal N[100,5]
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Contents
• Introduction– eBay auctions
• eBay Auction Revenue– Proxy bidding– Pedestrian bidding
• eBay Bid History– Number of observed bids– Bid timing
• Bidding Strategies– Sniping
• Conclusions
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Number of Observed Bids
• Proxy bidding causes the auction price to increase rapidly.
• Many bidders will not be able to submit a bid.valuation < current auction price + minimum bid increment
• N bidders attempt to place bids. • n bids accepted.• How is n related to N?
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Number of Observed Bids
HN – expected number of times that the second highest bid received so far changes.
• Add one more bid.
• Iterative solution.
• Standard asymptotic approximation.
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Number of Observed Bids
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Number of Observed Bids
• Number of bids accepted << Number of bidders attempting to place bids.
• eBay bid history is incomplete.
• Systematic errors when estimating:
– Bidders valuations.– Bidders strategies.
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Bid Timing
• eBay auctions are inefficient.
• Late bidding
– Increases the probability that bidders can’t submit a bid.
valuation < current auction price + minimum bid increment
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Bid Timing
20 biddersUniform [0,1]
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Contents
• Introduction– eBay auctions
• eBay Auction Revenue– Proxy bidding– Pedestrian bidding
• eBay Bid History– Number of observed bids– Bid timing
• Bidding Strategies– Sniping
• Conclusions
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Sniping
• Last minute bidding.• Prevents price wars with incremental bidders.• Doesn’t reveal private information.
• Automated through sniping software.• ‘Bid as late as possible.’
• But delaying bidding is disadvantageous.• Snipe but snipe before the snipers.
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Contents
• Introduction– eBay auctions
• eBay Auction Revenue– Proxy bidding– Pedestrian bidding
• eBay Bid History– Number of observed bids– Bid timing
• Bidding Strategies– Sniping
• Conclusions
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Conclusions
• Modelled the eBay auction protocol.
• Minimum bid increment + proxy bidding system = optimal auction revenue.
• eBay auction is inefficient.
• Bid history is incomplete – many hidden bidders.
• Delaying bidding is disadvantageous.
Snipe before the snipers