2 Auctions

7/30/2019 2 Auctions

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Auctions

If you learn about

Auction equivalencesYou'll save time online.


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Why use auctions?

Market forces are your new best friend!

Auctions can help determine how much

something is worth. (Ex: Keyword searches)

Auctions can prevent collusion.

Auctions can be used to sell something fast.

(The Aalsmeer flower auction conducts 50,000auctions each morningin the worlds largest

commercial buildingusing a Dutch auction.)


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Two types ofopen auctions

Ascending auction (a.k.a. English auction):

Price starts lowand goes up until Going once,

going twice, going three times, sold!

Examples: Silent auctions (usually), eBay, etc.

Descending auction (a.k.a. Dutch auction):

Price goes high and goes down until someone

indicates a willingness to buy.

Examples: Bargain basements (additional

10% off each week), Aalsmeer flower

auction.


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Dutch auction clock at Aalsmeer


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Two types of sealed-bid auctions

First-price sealed-bid auction: Highest bidder

wins and pays their own bid.

Second-price sealed-bid auction: Highest

bidder wins but only pays the second-highest

bid.

Example: Jane has the highest bid of $100 and

Mike is second with $90, so Jane wins but only

pays the $90.


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Aside: Multi-unit auctions

Many multi-unit auctions are generalized 2nd-

price sealed-bid auctions, i.e., you have 100

items to auction off so you take the top 100

bids and charge them all the 101st highest bid.

Example: Treasury auctions of public debt.

Example: Electricitysupply. (Enron?)

Example: Keywordsearches.

Example: Googles IPO.
http://www.newyorkfed.org/aboutthefed/fedpoint/fed41.htmlhttp://archive.ite.journal.informs.org/Vol4No1/FarrFelder/http://www.springer.com/economics/environmental/book/978-3-540-85364-0http://www.gsb.stanford.edu/news/research/econ_ostrovsky_internetauction.shtmlhttp://www2009.eprints.org/23/http://dealbook.blogs.nytimes.com/2009/08/19/googles-ipo-5-years-later/?hphttp://dealbook.blogs.nytimes.com/2009/08/19/googles-ipo-5-years-later/?hphttp://www2009.eprints.org/23/http://www.gsb.stanford.edu/news/research/econ_ostrovsky_internetauction.shtmlhttp://www.springer.com/economics/environmental/book/978-3-540-85364-0http://archive.ite.journal.informs.org/Vol4No1/FarrFelder/http://www.newyorkfed.org/aboutthefed/fedpoint/fed41.html


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Four types of auctions

Ascending: Price starts lowand goes up.

Descending: Price goes high and goes down.

First-price sealed-bid: Highest bidder wins andpays their own bid.

Second-price sealed-bid: Highest bidder

winner but only pays the second-highest bid. Questions: What are good bidding strategies

and which auction maximizes revenue?


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Second-price sealed-bid: Highest bidder wins

but only pays the second-highest bid. Questions: What are good bidding strategies?

Which auction maximizes revenue?


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Second-price sealed-bid: Highest bidder wins

but only pays the second-highest bid. Question: Why use a 2nd-price sealed-bid

auction when you can use a 1st-price one?


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True values

Assume each bidder has a true value that

doesnt change.

Your true value is your maximum willingness

to pay.

If my true value is $100, then Id be willing to

pay any amount less than $100 for the item, I

would not be willing to pay any amount more

than $100 for the item, and at a price of

exactly$100 Im indifferent.


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Bidding strategies (sealed-bid)

In a 1st-price sealed-bid auction, bidders do

not have a dominant strategy.

Example: In a first-price sealed-bid auction for

an item that you value at a max of $100, if the

highest bid other than yours is $50 then you

want to bid $51, and if the highest bid other

than yours is $20 then you want to bid $21.


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In a 1st-price sealed-bid auction, bidders do

not have a dominant strategy.

Theres no dominant strategy, but you

definitely want to shade your bid, i.e., bid less

than your true value.

If you dont shade your bid then youll never

get ahead!

How much to shade your bid is a difficult

question. (Do an expected value calculation!)


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In a 2nd-price sealed-bid auction, bidders do

have a dominant strategy: bid your true value!

Proof in a moment.

But first notice the implication for the

question about why youd want to use a 2nd-

price auction instead of a 1st-price auction.

You get higher bids in a 2nd-price auction!

So now its not clear which one is better


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Bidding your true value is a dominant strategy

means that you cannot do better regardless of

what others bid.


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Part I: If your true value is $100 and someone

bids more than your true value (say $125), can

you do better than bidding your true value?

No: The only way to win the auction involves

paying $125 or more for an item when your

maximum willingness to pay is only $100.


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Part II: If your true value is $100 and everyone

bids less than your true value, can you do

better than bidding your true value?

No: You only pay the second-highest bid, so

lowering your bid doesnt help you!

Look at the expected value calculation!


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Summary: Bidding less than your true value

doesnt help you; it just exposes you to the

risk of losing an auction youd like to win.

Bidding more than your true value doesnt

help you; it just exposes you to the risk of

winning an auction youd like to lose (youd

end up paying more than your true value).


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Auction equivalences

A descending auction is strategically

equivalentto a 1st-price sealed bid auction!

What is a bidders strategy in a descending

auction? If you have to go pee, what do you

tell Sam to do in order to bid for you?

Click the button or say Mine! at (say) $75.


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Now imagine that everyone has to go pee and

asks Sam to bid for them.

Sam can tell whos going to win!

The person with the highest bid is going to

win

and theyre going to pay their own bid.

So a descending auction is strategically

equivalentto a 1st-price sealed bid auction!


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An ascending auction is strategically

equivalentto a 2nd-price sealed bid auction!

What is a bidders strategy in an ascending

auction? If you have to go pee, what do you

tell Sam to do in order to bid for you?

Keep bidding but dont bid more than my true

value, which is (say) $100.

(Note the dominant strategy!)


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Now imagine that everyone has to go pee and

asks Sam to bid for them.

Sam can tell whos going to win!

The person with the highest bid is going to

win

but they only pay the 2nd-highest price!

So an ascending auction is strategically



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An ascending price auction is strategically


This is why eBay offers automatic bidding,

which turns ascending auctions into 2nd-price

sealed-bid auctions.

(Complication: Why do people often wait until

the last minute to submit eBay bids?)
http://pages.ebay.com/help/buy/automatic-bidding.htmlhttp://pages.ebay.com/help/buy/automatic-bidding.html


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Revenue equivalence theorem

We know that descending auctions are

strategically equivalent to 1st-price sealed-bid

auctions and that bidders will shade their

bids.

We know that ascending auctions are

strategically equivalent to 2nd-price sealed-bid

auctions and that bidding your true value is adominant strategy.

Which of these pairs is better for the seller?


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Revenue equivalence theorem

The revenue equivalence theorem says that in

many circumstances the expected revenue for

the seller is the same in all four types of

auctions!

Proof is too hard for this class, but a simple-ish

example is in Vickreys pioneering article.

2nd-price sealed bid auctions are sometimes

called Vickrey auctions in his honor.
http://www.wenli.net/teaching/752/Vickrey.pdfhttp://www.wenli.net/teaching/752/Vickrey.pdf


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Concluding thought

Market forces are your new best friend!

Try to get yourself to take your hand off the

steering wheel a bit

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2 Auctions