week 4 1 cos 444 internet auctions: theory and practice spring 2008 ken steiglitz...
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COS 444 COS 444 Internet Auctions:Internet Auctions:Theory and PracticeTheory and Practice
Spring 2008
Ken Steiglitz [email protected]
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TheoryTheory
First-Price equilibrium: IntuitionFirst-Price equilibrium: Intuition Third-Price equilibrium: IntuitionThird-Price equilibrium: Intuition Why study third-price auctions?Why study third-price auctions?
(Kagel-Levin 93, more later)(Kagel-Levin 93, more later)
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TheoryTheory
Equilibrium on First-Price auctionsEquilibrium on First-Price auctions
Baseline IPV model, values iid as Baseline IPV model, values iid as F F (v)(v)
E[surplus of 1] = E[surplus of 1] =
pr[1 wins][ pr[1 wins][ vv11 – b ( v – b ( v1 1 )) ] ]
Bidder 2 bids Bidder 2 bids (v) (v)
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TheoryTheory
The equilbrium condition is The equilbrium condition is thatthat
0/][ )()( vvbbsurplusE
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TheoryTheory
This leads to a linear, first-order This leads to a linear, first-order differential equation for differential equation for b(v)b(v) : :
vvFvfnbvFvfnb )](/)()1[()](/)()1[(
vvFvfnbvFvfnb )](/)()1[()](/)()1[(
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TheoryTheory
Solution:Solution:
… …optimal shadeoptimal shade
vvFvfnbvFvfnb )](/)()1[()](/)()1[(
)1(
0
)1( )(/)()( nv n yFdyyFvvb
)1(
0
)1( )(/)()( nv n vFdyyFvvb
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eBay observedeBay observed
Assignment 2 provides a tool for Assignment 2 provides a tool for visualizing behavior…visualizing behavior…
Some examples:Some examples:
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Early bidding vs. Early bidding vs. SnipingSniping• But But early biddingearly bidding
affects behavioraffects behavior
WAR
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Dangers of early Dangers of early bidding, con’tbidding, con’t
As bait
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Dangers of early Dangers of early bidding, con’tbidding, con’t
Curiosity
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A (likely) shillA (likely) shill
• Bidder 3 bids Bidder 3 bids $94 when $94 when the reserve the reserve is $95 and is $95 and the high bid the high bid is below is below that. She that. She has has feedback of feedback of 1. A likely 1. A likely shill.shill.
Reserve = $95 ______
