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![Page 1: Incentive Auctions Peter Cramton* Professor of Economics, University of Maryland Chairman, Market Design Inc. 23 May 2011 (updated 29 May 2011) * Special.](https://reader034.fdocuments.in/reader034/viewer/2022052618/55195a86550346a5698b46c1/html5/thumbnails/1.jpg)
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Incentive AuctionsPeter Cramton*
Professor of Economics, University of MarylandChairman, Market Design Inc.
23 May 2011 (updated 29 May 2011)* Special thanks to Larry Ausubel, Evan Kwerel, and Paul Milgrom for collaborating with me on this topic over the last dozen years. Thanks to the National Science Foundation for funding.
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Incentive auctions
High value
Mobile broadband
Low value
Over-the-air TV broadcast
Auction includes essential regulatory steps to address market failures in the secondary market for spectrum
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Letter from 112 economists, 6 April 2011
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Motivation
Year
Value per MHz
1985 1990 1995 2000 2005 2010 2015
Value of over-the-air broadcast TV
Value of mobile broadband
TV signal received via cable
and satellite
Expl
osio
n in
use
of
smar
tpho
nes a
nd ta
blet
s
Gains
from trad
e
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VHF and UHF bands
54 88 174
216470
698
512
614608
37
Lower VHF Upper VHF UHF
Public Safety
Current uses (TV broadcast)Current uses (TV broadcast)
TV ch 2-6 TV ch 7-13 TV ch 14-36
RA
54 88 174
216470
698
512
614608
37
Lower VHF Upper VHF UHF
Public Safety
Possible future usesPossible future uses
TV ch 2-6 TV ch 7-13 TV ch 14-??
RA
Flexible UseFlex. Use
TV ch 38-51
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Voluntary approachTV
broadcaster freely decides
to
Shar
e w
ith a
noth
er
Cease over-the-air
broadcast
Conti
nue
over
-the-
air b
road
cast
0 MHz 3 MHz 6 MHzSpectrum freed
For simplicity, I assume that channel sharing is only 2:1; other possibilities could also be considered, including negotiated shares with particular partners announced at qualification
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Why voluntary?• More likely to quickly clear spectrum
– Broadcasters benefit from cooperating• Lower economic cost of clearing
– Spectrum given up only by broadcasters who put smallest value on over-the-air signal
• Market pricing for clearing– Avoids costly administrative process
• Efficient clearing– Clear only when
value to mobile operator > value to TV broadcaster
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Two approaches
Combinatorial exchange
Too complex due to
repacking
Reverse auction to determine
supplyForward
auction to determine demand
Optimiza-tion gives
mandatory repacking options
Market clearing and settlement
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• Mostly single channel• Price discovery less
important=>• Sealed-bid auction or
descending clock– Price to cease– Price to share
TV broadcaster
freely decides to
Shar
e w
ith a
noth
er
Cease over-the-air
broadcast
Conti
nue
over
-the-
air b
road
cast
0 MHz 3 MHz 6 MHzSpectrum freed
Reverse auction to determine
supply
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Reverse auction to determine
supply
13
22
0 MHz
7
31
37 41
3 MHz
9 2618
354447
6 MHz
Price = $30/MHzPopP = $30
S = 48
Washington DC
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713
3122
Reverse auction to determine
supply
9 26
37 4118
354447
0 MHz 3 MHz 6 MHz
Price = $20/MHzPopP = $20
S = 36
Washington DC
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713
3122
Reverse auction to determine
supply
9 26
37 4118
354447
0 MHz 3 MHz 6 MHz
Price = $10/MHzPopP = $10
S = 24
Washington DC
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Mandatory repacking
7 13
3122
9 26
37 4118
354447
57
119
13 1315 15
S = 36P = $20 Supply =
160 MHz
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Forward auction to determine demand
• Mobile operators want large blocks of contiguous paired spectrum for LTE (4G)– One to four 2 × 5 MHz lots
• Complementaries strong both within and across regions
• Package clock auction ideal– Within region complementarities
guaranteed with generic lots– Across region complementarities
achieved through optimization of specific assignments
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Package clock auction: Overview• Auctioneer names prices; bidder names package
– Price increased if there is excess demand– Process repeated until no excess demand
• Supplementary bids– Improve clock bids– Bid on other relevant packages
• Optimization to determine assignment/prices
• No exposure problem (package auction)• Second pricing to encourage truthful bidding• Activity rule to promote price discovery
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Forward auction to determine demand
Quantity
Price
P2
P3
P4
P5
P6Supply
P0
P1
Demand
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Forward auction to determine demand
Quantity
Price Supply
P*
Q*
Demand
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To Treasury
To TV broadcasters
Forward auction to determine demand
Quantity
Price Supply
PD
Q0
PS
Q*
Broadcasters cannot negotiate ex post with operators, since it is the
FCC’s repacking that creates value; ex post trades would not
benefit from repacking
Demand
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Ways Congress can screw up
• Impose restrictions on which broadcasters can participate in the auction– Destroys competition in reverse auction
• Make repacking purely voluntary– Reverses status quo—FCC can relocate stations– Creates holdout problem in reverse auction
• Too greedy– Impose specific requirement on government
revenue share (e.g., Treasury gets 40% of revenue)
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To Treasury
To TV broadcasters
Quantity
Price
Supply
PD
Q0
PS
Q*
Not too greedy:Quantity choice left to FCC
Demand
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21Quantity
Price
Supply
PD
Q40%
PS
Q*
Too greedy constraint:Treasury must get at least 40%
DemandTo Treasury
To TV broadcasters
Revenue share constraint causes huge social welfare loss and reduces Treasury revenues!
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Ways FCC can screw up
• Impose restrictions on which broadcasters can participate in the auction– Destroys competition in reverse auction
• Make repacking purely voluntary– Reverses status quo—FCC can relocate stations– Creates holdout problem in reverse auction
• Adopt poor auction design• Fail to address competition concerns
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Background
Package Clock Auction
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Package clock auction: Overview
• A package bid is an all-or-nothing bid for a portfolio of products
• When bidding on individual lots, a bidder is exposed to the risk of winning only some of a complementary set of products
• Package bidding eliminates the exposure problem by allowing bidders to bid on packages of products
• At the same time, package bidding can help to alleviate the demand reduction problem in which larger bidders inefficiently reduce demand in order to win spectrum at lower prices
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Package clock auction: Overview• Auctioneer names prices; bidder names package
– Price increased if there is excess demand– Process repeated until no excess demand
• Supplementary bids– Improve clock bids– Bid on other relevant packages
• Optimization to determine assignment/prices
• No exposure problem (package auction)• Second pricing to encourage truthful bidding• Activity rule to promote price discovery
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Package clock auction adopted for several recent and upcoming auctions
• UK 10-40GHz spectrum– February 2008, 27 rounds, £16 million
• UK L-band spectrum– May 2008, 33 rounds, £8.3 million
• UK 800MHz and 2.6GHz– First-quarter 2012
• Netherlands 2.6GHz spectrum• Belgium 2.6GHz spectrum• Austria 2.6GHz spectrum
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Bidder-optimal core pricing
• Minimize payments subject to core constraints• Core = assignment and payments
such that– Efficient: Value maximizing assignment– Unblocked: No subset of bidders offered seller a
better deal
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Five-bidder example with bids on {A,B}
• b1{A} = 28
• b2{B} = 20
• b3{AB} = 32
• b4{A} = 14
• b5{B} = 12
Winners
Vickrey prices:p1= 14
p2= 12
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The Core
b4{A} = 14
b3{AB} = 32
b5{B} = 12
b1{A} = 28
b2{B} = 20
Bidder 2Payment
Bidder 1Payment
14
12
3228
20
The Core
Efficient outcome
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The Core
b4{A} = 14
b3{AB} = 32
b5{B} = 12
b1{A} = 28
b2{B} = 20
Bidder 2Payment
Bidder 1Payment
Vickrey prices
14
12
3228
20
Vickrey prices: How much can each winner’s bid be reduced (while holding others fixed)?
Problem: Bidder 3 can offer seller more (32 > 26)!
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The Core
b4{A} = 14
b3{AB} = 32
b5{B} = 12
b1{A} = 28
b2{B} = 20
Bidder 2Payment
Bidder 1Payment
Vickrey prices
14
12
3228
20
Bidder-optimal core prices: Jointly reduce winning bids as much as possible (while remaining within core)
Bidder-optimal core
Problem: bidder-optimal core prices are not unique!
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Uniquecore prices
b4{A} = 14
b3{AB} = 32
b5{B} = 12
b1{A} = 28
b2{B} = 20
Bidder 2Payment
Bidder 1Payment
Vickrey prices
14
12
3228
20
Core point closest to Vickrey prices(Alternative: core point closest to linear prices)
17
15
Each pays equal share above Vickrey
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Package clock auctions: Activity rule
• Activity rule based on revealed preference:Bidders can only move toward packages that become better values– At time t > t, package qt has become relatively
cheaper than qt (P) qt(pt – pt) qt(pt – pt)
– Supplementary bid b(q) must be less profitable than revised package bid at t(S) b(q) b(qt) + (q – qt)pt
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Properties with substitutes
• Bidding on most profitable package is best• Clock yields competitive equilibrium with
efficient assignment and supporting prices• Final assignment = clock assignment
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Properties in general
• Supplementary bids needed if excess supply• Bidder can guarantee winning its final package
by raising bid by final price of unsold lots