Week 31 COS 444 Internet Auctions: Theory and Practice Spring 2010 Ken Steiglitz...
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Transcript of Week 31 COS 444 Internet Auctions: Theory and Practice Spring 2010 Ken Steiglitz...
week 3 2
Theory
• Order statistics
pdf of k-th highest
cdf of k-th highest
• Application to revenue calculation
week 3 3
pdf of k-th largest
1))(1( kxF
knxF )(
n choices for which drawn
1
1
k
n
1
1
k
nn f(x) dx 1))(1( kxF knxF )(
ways
week 3 4
knkk xFxFxf
k
nnxg
)())(1)((1
1)( 1
11 )()()( nxFxfnxg
nxFxG )()(1
22 )())(1)(()1()( nxFxFxfnnxg
nn xFnxnFxG )()1()()( 12
week 3 5
German tank problem
Nk
kdxxkxNdxxxgNEM k
1)([max]
1
0
11
0 1
Suppose tank numbers are sequential real numbers uniformon [0,N]. We capture k tanks. The expected max of k samples is
So a reasonable estimate is
Mk
kN
1 (when values are
integers, subtract 1)
week 3 6
Theory
• Order statistics
pdf of k-th highest
cdf of k-th highest
• Simple equilibrium calculation
week 3 7
bbbv
bvn 1
1
1
)/()(
}wins1{prob)(]surplus[E
First price, n biddersSuppose everyone else bids θvi
Differentiate wrt b, set to 0 b = (1-1/n)v1
(checks )b
so θ = (1-1/n) works as equilibrium
Quick and dirty equilibrium calculation for FP with iid uniform values
week 3 8
Theory
• Order statistics
pdf of k-th highest
cdf of k-th highest
• Simple equilibrium calculation
• Revenue equivalence w. uniform v’s
week 3 9
Revenue equivalence of FP & SP, uniform
• SP:
E[price paid] = E[Y2] = (n-1)/(n+1)
E[value of winner] = E[Y1] = n/(n+1)E[surplus of winner] = difference = 1/(n+1)
• FP:Equil. Bid is v*(n-1)/n
E[surplus of winner] = E[vmax/n] = 1/(n+1)
week 3 10
New directions: Sociology
M. Shohat and J. Musch “Online auctions as a research tool: A field experiment on ethnic discrimination” Swiss Journal of Psychology 62 (2), 2003, 139-145
week 3 11
Shohat & Musch ’03 typical field experiment
methodology
• Parallel items sold (30 DVDs), once with each experimental variable (mehmet.orgum vs. michael.ottersbach); and all other variables controlled as equal or randomized.
Eg., Mehmet auctioned one randomly chosen half (A) the first week, and the other half (B) the second week; Michael auctioned B the first week and A the second.
week 3 12
Shohat & Musch ’03 typical field experiment
methodology
• Other variables controlled as carefully as possible (for example, DVDs not shipped first week, so no feedback appeared for either “seller”)
• Statistical tests of results (usually probability of observing results assuming null hypothesis > 95%)
week 3 13
Shohat & Musch ’03 typical field experiment
methodology
Discussion, interpretation• Alternative explanations (not high enough
financial risk; not social setting; “Mehmet” not recognized as Turk; presentation might have seemed “German” (!); buyers may turn to Turkish sellers only after not finding it from a German seller, etc.)
• Other work
week 3 14
Shohat & Musch ’03 typical field experiment methodology
Privacy, ethics: Buyers not informed, no consent!
• Data hidden after experiment (“make profile private”, anonymity guaranteed)
• Experiments kept within rules (no surveys, eg)
• Deals kept scrupulously honest
week 3 15
Field experiments: Testing theory
• LR 99: tests FP-Dutch and SP-English revenue equivalence online (pre-eBay)
• Katkar-LR 00: tests public vs. secret reserve on eBay
• LR 00: tests effects of reserves in FP online (pre-eBay)
week 3 16
Lucking-Reiley 99:Magic on the internet(his PhD dissertation)
• Pre-eBay
• Tests revenue equivalence:
FP=Dutch and
SP=English
week 3 17
LR 99 (con’t)
• Newsgroup: rec.games.deckmaster, now an impossible experiment.
• 1995: 6000 messages/week, highest volume on the internet. 90% Magic cards.
• Variety of auctions observed, all but Vickrey• Sold matched pairs, first with FP first, then
Dutch; then with Dutch first, then FP. Similarly for English-SP.
• Experiments were profitable…$1600 purchase sold for $2000.
week 3 18
LR 99 (con’t)
Results:• Revenue in Dutch > FPDutch > FP by 30% (opposite to lab experiments) Explain! (while strategically equilvalent)• Revenue in English English ≈ SP≈ SP (while weakly strategically equivalent)• Revenue equivalence between pairs left open