Peter Cramton Professor of Economics University of Maryland Chairman 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 Found ID: 386812
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Slide1
Incentive Auctions
Peter 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.
1Slide2
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
2Slide3
Letter from 112 economists, 6 April 2011
3Slide4
Motivation
Year
Value per MHz1985
1990
1995
2000
2005
2010
2015
Value of over-the-air broadcast TV
Value of mobile broadband
TV signal received via cable and
satellite
Explosion in use of smartphones and tablets
Gains from trade
4Slide5
VHF and UHF
bands
54
88
174
216
470
698
512
614
608
37
Lower VHF
Upper VHF
UHF
Public Safety
Current u
ses (TV broadcast)
TV ch 2-6
TV ch 7-13
TV ch 14-36
RA
54
88
174
216
470
698
512
614
608
37
Lower VHF
Upper VHF
UHF
Public Safety
Possible
future
u
ses
TV ch 2-6
TV ch 7-13
TV ch 14-??
RA
Flexible Use
Flex. Use
TV ch 38-51
5Slide6
Voluntary approach
TV broadcaster freely decides toShare with another
Cease over-the-air broadcast
Continue over-the-air broadcast
0 MHz
3
MHz
6
MHz
Spectrum freed
6
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 qualificationSlide7
Why voluntary?More likely to quickly clear spectrum
Broadcasters benefit from cooperatingLower economic cost of clearingSpectrum given up only by broadcasters who put smallest value on over-the-air signalMarket pricing for clearingAvoids costly administrative process
Efficient clearingClear only whenvalue to mobile operator > value to
TV broadcaster
7Slide8
Two approaches
Combinatorial exchange
Too complex due to repacking
Reverse auction to determine supply
Forward auction to determine demand
Optimiza-tion
gives mandatory repacking options
8
Market clearing and settlementSlide9
Mostly single channelPrice discovery less important=>Sealed-bid auction or descending clockPrice to ceasePrice to share
TV broadcaster freely decides to
Share with another
Cease over-the-air broadcast
Continue over-the-air broadcast
0 MHz
3
MHz
6
MHz
Spectrum freed
Reverse auction to determine supply
9Slide10
Reverse auction to determine supply
13
22
0 MHz
7
31
37
41
3
MHz
9
26
18
35
44
47
6
MHz
Price = $30/MHzPop
P = $30
S = 48
Washington DC
10Slide11
7
13
31
22
Reverse auction to determine supply
9
26
37
41
18
35
44
47
0 MHz
3
MHz
6
MHz
Price = $20/MHzPop
P = $20
S = 36
Washington DC
11Slide12
7
13
31
22
Reverse auction to determine supply
9
26
37
41
18
35
44
47
0 MHz
3
MHz
6
MHz
Price = $10/MHzPop
P = $10
S = 24
Washington DC
12Slide13
Mandatory repacking
7
13
31
22
9
26
37
41
18
35
44
47
5
7
11
9
13
13
15
15
S = 36
P = $20
Supply = 160 MHz
13Slide14
Forward auction to determine demand
Mobile operators want large blocks of contiguous paired spectrum for LTE (4G)One to four 2 × 5 MHz lotsComplementaries strong both within and across regionsPackage clock auction idealWithin region complementarities guaranteed with generic lotsAcross region complementarities achieved through optimization of specific assignments
14Slide15
Package clock auction: OverviewAuctioneer names prices; bidder names package
Price increased if there is excess demandProcess repeated until no excess demandSupplementary bidsImprove clock bidsBid on other relevant packagesOptimization to determine assignment/prices
No exposure problem (package auction)Second pricing to encourage truthful biddingActivity rule to promote price discovery
15Slide16
Forward auction to determine demand
Quantity
Price
P
2
P
3
P
4
P
5
P
6
Supply
P
0
P
1
Demand
16Slide17
Forward auction to determine demand
Quantity
Price
Supply
P*
Q*
17
DemandSlide18
To Treasury
To TV broadcasters
Forward auction to determine demand
Quantity
Price
Supply
P
D
Q
0
P
S
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
18
DemandSlide19
Ways Congress can screw upImpose restrictions on which broadcasters can participate in the auctionDestroys competition in reverse auctionMake repacking purely voluntary
Reverses status quo—FCC can relocate stationsCreates holdout problem in reverse auctionToo greedyImpose specific requirement on government revenue share (e.g., Treasury gets 40% of revenue)19Slide20
To Treasury
To TV broadcasters
Quantity
Price
Supply
P
D
Q
0
P
S
Q*
Not too greedy:
Quantity choice left to FCC
20
DemandSlide21
Quantity
Price
Supply
P
D
Q
40%
P
S
Q*
Too greedy constraint:
Treasury must get at least 40%
21
Demand
To Treasury
To TV broadcasters
Revenue share constraint causes huge social welfare loss
and
reduces Treasury revenues!Slide22
Ways FCC can screw upImpose restrictions on which broadcasters can participate in the auctionDestroys competition in reverse auctionMake repacking purely voluntary
Reverses status quo—FCC can relocate stationsCreates holdout problem in reverse auctionAdopt poor auction designFail to address competition concerns22Slide23
BackgroundPackage Clock Auction
23Slide24
Package clock auction: OverviewA package bid is an all-or-nothing bid for a portfolio
of productsWhen bidding on individual lots, a bidder is exposed to the risk of winning only some of a complementary set of productsPackage bidding eliminates the exposure problem by allowing bidders to bid on packages of productsAt 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
24Slide25
Package clock auction: OverviewAuctioneer names prices; bidder names package
Price increased if there is excess demandProcess repeated until no excess demandSupplementary bidsImprove clock bidsBid on other relevant packagesOptimization to determine assignment/prices
No exposure problem (package auction)Second pricing to encourage truthful biddingActivity rule to promote price discovery
25Slide26
Package clock auction adopted for several recent and upcoming auctionsUK 10-40GHz spectrumFebruary 2008, 27 rounds, £16 million
UK L-band spectrumMay 2008, 33 rounds, £8.3 millionUK 800MHz and 2.6GHzFirst-quarter 2012Netherlands 2.6GHz spectrumBelgium 2.6GHz spectrumAustria 2.6GHz spectrum26Slide27
Bidder-optimal core pricingMinimize payments subject to core constraintsCore = assignment and payments
such thatEfficient: Value maximizing assignmentUnblocked: No subset of bidders offered seller a better deal27Slide28
Five-bidder example with bids on {A,B}
b
1
{A} = 28
b
2
{B} = 20
b
3
{AB} = 32
b
4
{A} = 14
b
5
{B} = 12
Winners
Vickrey prices:
p
1
= 14
p
2
= 12
28Slide29
The Core
b
4
{A} = 14
b
3
{AB} = 32
b
5
{B} = 12
b
1
{A} = 28
b
2
{B} = 20
Bidder 2
Payment
Bidder 1
Payment
14
12
32
28
20
The Core
Efficient outcome
29Slide30
The Core
b
4
{A} = 14
b
3
{AB} = 32
b
5
{B} = 12
b
1
{A} = 28
b
2
{B} = 20
Bidder 2
Payment
Bidder 1
Payment
Vickrey prices
14
12
32
28
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)!
30Slide31
The Core
b
4
{A} = 14
b
3
{AB} = 32
b
5
{B} = 12
b
1
{A} = 28
b
2
{B} = 20
Bidder 2
Payment
Bidder 1
Payment
Vickrey prices
14
12
32
28
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!
31Slide32
Unique
core prices
b
4
{A} = 14
b
3
{AB} = 32
b
5
{B} = 12
b
1
{A} = 28
b
2
{B} = 20
Bidder 2
Payment
Bidder 1
Payment
Vickrey prices
14
12
32
28
20
Core point closest to Vickrey prices
(Alternative: core point closest to linear prices)
17
15
Each pays equal share above Vickrey
32Slide33
Package clock auctions: Activity ruleActivity rule based on revealed preference:
Bidders can only move toward packages that become better valuesAt time t > t, package qt has become relatively cheaper than qt (P
) qt(pt
– p
t
)
q
t
(p
t – pt)
Supplementary bid b(q) must be less profitable than revised package bid at t(S) b(q) b(q
t
) + (q – q
t
)p
t
33Slide34
Properties with substitutesBidding on most profitable package is bestClock yields competitive equilibrium with efficient assignment and supporting prices
Final assignment = clock assignment34Slide35
Properties in generalSupplementary bids needed if excess supplyBidder can guarantee winning its final package by raising bid by final price of unsold lots
35