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