spectrum auction design
TRANSCRIPT
Spectrum Auction Design
Peter Cramton Professor of Economics, University of Maryland
www.cramton.umd.edu/papers/spectrum
1
Two parts
• One-sided auctions
• Two-sided auctions (incentive auctions)
2
Application: Spectrum auctions
• Many items, heterogeneous but similar
• Competing technologies
• Complex structure of substitutes and complements
• Long-term market
• Government objective: Efficiency – Make best use of scarce spectrum
• Recognizing competition issues in downstream market
Main points
• Enhance substitution – Product design
– Auction design
• Encourage price discovery – Dynamic price process to focus valuation efforts
• Induce truthful bidding – Pricing rule
– Activity rule
Simultaneous ascending auction
• Simultaneous
– All lots at the same time
• Ascending
– Can raise bid on any lot
• Stopping rule
– All lots open until no bids on any lot
• Activity rule
– Must be active to maintain eligibility
Simultaneous ascending auction
• Strengths – Simple price discovery process
– Allows arbitrage across substitutes
– Piece together desirable packages
– Reduces winner’s curse
• Weaknesses – Demand reduction
– Tacit collusion
– Parking
– Exposure
– Hold up
– Limited substitution
– Complex bidding strategies
Rigid band plans: something for everyone
Uplink C D E
Bandwidth 10 MHz 10 MHz 10 MHz
Partition Medium Large Large
Regions 176 12 12
Downlink C D E
17551740
2110 2120 2130 2140 2155
734 176 12
A B F
Small Medium Large
1710 1720 1730
US AWS band plan: something for everyone
A B F
20 MHz 20 MHz 20 MHz
AWS price for 10 MHz by block
0M 100M 200M 300M 400M 500M 600M 700M 800M 900M 1000M 1100M 1200M 1300M 1400M 1500M 1600M 1700M 1800M 1900M 2000M 2100M
High Bids per 10 MHz
8
A
B
C
D
E
F
12
A
B
C
D
E
F
16
A
B
C
D
E
F
31
A
B
C
D
E
F
161
A
B
C
D
E
F
license_size_mhz
10
20
Sum of pwb amount per 10 MHz for each block broken down by round. Color shows details about pw_bidder. Size shows details about license_size_mhz. The view is filtered on pw_bidder and round. The pw_bidder filter excludes . The round filter keeps 8, 12, 16, 31 and 161.
Day 3
Day 4
Day 5
Stage 2
Final
40% discount
6 REAGs
176 EAs 734 CMAs
Limited substitution: 700 MHz 62 MHz, 261 rounds, $19.6 billion
Verizon AT&T
Verizon and AT&T won 85% of spectrum
Block A B C
Bandwidth 12 MHz 12 MHz 22 MHz
Type paired paired paired
Partition 176 734 12
Price $1.16 $2.68 $0.76
German 4G Auction: 360 MHz, 224 rounds, €4.4 billion
800 Winner A B C D E F T-Mobile Vodafone O2 E-plus
Final bid 616,595 595,760 570,849 582,949 583,005 627,317
1.8 Winner A B C 2x5 MHz D 2x5.4 MHz E
Final bid 20,700 20,700 19,869 21,550 21,536
2.0 WinnerE
TDD
5 MHz
TDD
5 MHz
TDD
5 MHz
TDDA B C D
Final bid 5,731 93,757 103,323 84,064 66,931
2.6 Winner A B C D E F G H I J K L M N
Final bid 19,096 19,025 17,364 17,364 18,948 19,025 19,069 19,038 18,948 18,931 17,739 17,739 17,739 17,752
2.6 Winner O P Q R S T U V W X
TDD Final bid 9,130 9,130 8,598 8,598 9,051 9,051 8,273 8,229 8,229 8,229
F
TDD5,715
2x10 MHz
2x17.4 MHz
2x10 MHz 2x10 MHz 2x10 MHz
2x17.4 MHz
800 MHz 1.8 GHz 2.0 GHz 2.6 GHz 2.0 GHz E 2.0 GHz F 2.6 GHz TDD
0.729 0.026 0.106 0.023 0.014 0.005 0.021
Average Price in Each Band (€/MHz-pop)
German 4G auction key features
• Full transparency
• Low reserve prices
• Bidders clearly signaled outcome in 1st round
• Only conflict was E-plus 1 lot at 800 MHz
• Auction conducted on-site with 1980 software that failed after the first round
11
Italy 4G Auction, Final Outcome 470 rounds, 22 days, €3.95B
800
MHz
1,800
MHz
2,600
GHz
2,000
MHz
TDD
2,600
MHz
TDD
800
MHz
1,800
MHz
2,600
GHz
2,000
MHz
TDD
2,600
MHz
TDD
W 1,119.92 1,119.92 2 (s) 4 (s) 0.812 0.059
T 1,260.32 1,260.32 2 1 3 0.824 0.264 0.060
V 1,259.68 1,259.68 2 1 3 0.824 0.264 0.060
H 305.38 305.38 1 2 2 0.264 0.060 0.041
800
MHz800_S 800G 800G 800G 800G 800G
481.70 496.00 496.10 496.10 496.20 496.20
1,800
MHz1800G 1800G 1800G
159.00 159.10 158.90
2,000 MHz
2,600 MHz
FDD2600G 2600G 2600G 2600G 2600G 2600G 2600G 2600G 2600G 2600G 2600G 2600_S
36.40 36.40 36.32 36.06 36.06 36.06 36.40 36.04 36.36 36.02 36.02 33.82
2,600 MHz
TDD
Price (euro) per MHz-PopNumber of lots won
Round 469
2600B 2600C
37.20 36.84
2000A
77.93
Total
bid
submitted
Total
winning
bid
Players
No bids
12
Italy 4G Auction Key features
• Full transparency
• Ranking list for each category (provisional winners)
• No activity rule
• 800 closes after 3 rounds without bids in any category
• Auction closes after 5 rounds without any bids in any category – Makes this a sequential auction: 800 then other bands,
since 800 must close first
• Auction conducted on-site with pen and paper
13
Combinatorial Clock Auction
14
Needed enhancements
• Anonymous bidding
• Generic lots
• Package bidding with clock
– Porter-Rassenti-Roopnarine-Smith (2003)
– Ausubel-Cramton (2004)
– Ausubel-Cramton-Milgrom (2006)
• “Second” pricing
• Revealed preference activity rule
Combinatorial clock auction
• Auctioneer names prices; bidder names package – Price increased if 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
16
UK spectrum auctions
UK auctions
10-40 GHz: fixed wireless or backhaul
L-Band: mobile broadcast
• 2.6 GHz: 4G mobile wireless (2013)
• Digital Dividend: 4G, mobile TV, DTT (2013)
Requirements
• Technology neutral
• Flexible spectrum usage rights
• Efficient assignment
UK 2.6 GHz auction
• 190 MHz (38 lots of 5 MHz)
• How much paired vs. unpaired?
CEPT band plan from Electronic Communications Committee Decision (05)05Type
Lot 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Frequency
2
5
0
0
2
5
0
5
2
5
1
0
2
5
1
5
2
5
2
0
2
5
2
5
2
5
3
0
2
5
3
5
2
5
4
0
2
5
4
5
2
5
5
0
2
5
5
5
2
5
6
0
2
5
6
5
2
5
7
0
2
5
7
5
2
5
8
0
2
5
8
5
2
5
9
0
2
5
9
5
2
6
0
0
2
6
0
5
2
6
1
0
2
6
1
5
2
6
2
0
2
6
2
5
2
6
3
0
2
6
3
5
2
6
4
0
2
6
4
5
2
6
5
0
2
6
5
5
2
6
6
0
2
6
6
5
2
6
7
0
2
6
7
5
2
6
8
0
2
6
8
5
Paired (FDD uplink) Paired (FDD downlink)Unpaired (TDD)
Let auction determine band plan
Increase in unpaired spectrum maintaining 120 MHz duplex spacingType
Lot 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 15 16 17 18
Frequency
2
5
0
0
2
5
0
5
2
5
1
0
2
5
1
5
2
5
2
0
2
5
2
5
2
5
3
0
2
5
3
5
2
5
4
0
2
5
4
5
2
5
5
0
2
5
5
5
2
5
6
0
2
5
6
5
2
5
7
0
2
5
7
5
2
5
8
0
2
5
8
5
2
5
9
0
2
5
9
5
2
6
0
0
2
6
0
5
2
6
1
0
2
6
1
5
2
6
2
0
2
6
2
5
2
6
3
0
2
6
3
5
2
6
4
0
2
6
4
5
2
6
5
0
2
6
5
5
2
6
6
0
2
6
6
5
2
6
7
0
2
6
7
5
2
6
8
0
2
6
8
5
All unpaired spectrumType
Lot 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38
Frequency
2
5
0
0
2
5
0
5
2
5
1
0
2
5
1
5
2
5
2
0
2
5
2
5
2
5
3
0
2
5
3
5
2
5
4
0
2
5
4
5
2
5
5
0
2
5
5
5
2
5
6
0
2
5
6
5
2
5
7
0
2
5
7
5
2
5
8
0
2
5
8
5
2
5
9
0
2
5
9
5
2
6
0
0
2
6
0
5
2
6
1
0
2
6
1
5
2
6
2
0
2
6
2
5
2
6
3
0
2
6
3
5
2
6
4
0
2
6
4
5
2
6
5
0
2
6
5
5
2
6
6
0
2
6
6
5
2
6
7
0
2
6
7
5
2
6
8
0
2
6
8
5
Unpaired (TDD)
UnpairedPaired (FDD uplink) Unpaired (TDD) Paired (FDD downlink)
Key design choices • Generic 5 MHz lots
– Lots are perfect substitutes
• Package bids – No exposure problem
• Clock stage – How many paired? How many unpaired? Supply = 38 – Continue until no excess demand
• Supplementary bids – Improve clock bids; add other packages
• Principal stage – Find value maximizing generic assignment and base prices
• Assignment stage – Contiguous spectrum – Top-up bid to determine specific assignment
Pricing rule
22
Pricing rule
• In clock stage? In assignment stage?
• Pay-as-bid pricing
– Incentives for demand reduction, bid shading
• Bidder-optimal core pricing
– Maximize incentives for truthful bidding
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 offerred seller a better deal
24
Optimization
• Core point that minimizes payments readily calculated
– Solve Winner Determination Problem
– Find Vickrey prices
– Constraint generation method (Day and Raghavan 2007) • Find most violated core constraint and add it
• Continue until no violation
• Tie-breaking rule for prices is important
– Minimize distance from Vickrey prices
25
5 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
26
The Core
b4{A} = 14
b3{AB} = 32
b5{B} = 12
b1{A} = 28
b2{B} = 20
Bidder 2
Payment
Bidder 1
Payment
14
12
32 28
20
The Core
Efficient outcome
27
The Core
b4{A} = 14
b3{AB} = 32
b5{B} = 12
b1{A} = 28
b2{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 holding others fixed?
Problem: Bidder 3
can offer seller
more (32 > 26)!
28
The Core
b4{A} = 14
b3{AB} = 32
b5{B} = 12
b1{A} = 28
b2{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
Problem: bidder-
optimal core prices
are not unique!
29
Unique
core prices
b4{A} = 14
b3{AB} = 32
b5{B} = 12
b1{A} = 28
b2{B} = 20
Bidder 2
Payment
Bidder 1
Payment
Vickrey
prices
14
12
32 28
20
Core point closest to Vickrey prices
17
15
Each pays
equal share
above Vickrey
30
Activity rule
31
Activity rule: Eligibility points
• Clock stage: Cannot increase package size
• Supplementary bids: Whenever reduce package size, value on all larger packages capped by prices at time of reduction
– Example • Bidder drops from package of size 10 to 6 at prices p
• For all packages q of size 7 to 10, bid q p
• Implication
– Profit maximization is poor strategy
– Bid to maximize package size subject to profit 0
Full-scale test of design (Maryland and GMU PhD students)
• Experienced subjects
– PhD course in game theory and auctions
– Prior participation in combinatorial clock auction
• Motivated subjects
– Average subject payment = $420
• Realistic scenarios
Result
• Activity rule causes major deviation from straightforward bidding
– Undermines price discovery
– Reduces efficiency
Activity rule readily fixed: Revealed preference
• 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
Example • Revealed preference
– Bid on most profitable package (max profit)
– Move up marginal value (demand) curve
• Eligibility point – Bid on largest profitable package (max size)
– Move up average value curve
Each wins one; price = 2
Competitive equilibrium!
A wins both; price = 8
Too concentrated; too high priced!
Bidder
A
Bidder
B
Bidder
A
Bidder
B
1 lot 16 8 16 8
2 lots 2 2 9 5
Marginal Value Average Value
Demand downward sloping Average value > marginal value
Average
Value
Marginal
Value
Supply
Quantity
Price
Eligibility point price
Revealed preference price =
Competitive equilibrium price
Activity rule based on eligibility points and revealed preference
• Clock stage
– Can always shift to smaller packages
– Can shift to a larger package that has become relatively cheaper
• Supplementary bids
– Final price cap: All packages q are capped by revealed preference with respect to final clock package qf
– Packages q larger than qf are also capped by revealed preference with respect to each eligibility reducing round beginning with round in which bidder first bid for a package smaller than q
( ) ( ) ( )f f fb q b q q q p
38
Clock stage performs well Proposition:
If clock stage ends with no excess supply, final assignment = clock assignment
Supplementary bids can’t change assignment; but can change prices
• May destroy incentive for truthful bidding in
supplementary round • Supplementary round still needed to determine
competitive prices • Solution: Do not reveal demand at end of clock stage
39
Properties with substitutes
• Bidding on most profitable package is best
• Clock yields competitive equilibrium with efficient assignment and supporting prices
• Final assignment = clock assignment
40
Properties in general
• Supplementary bids needed
– To identify efficient assignment
– To determine competitive prices
41
Missing bids problem
• With many products, optimizer may have too few bids for efficiency and competitive pricing – Number of packages explodes with products
• Regional products (US, Canada, Australia) imply many products
• Need better way to express preferences – Value tables that are additive across regions
– Bidder expresses value for each regional package • Bidder value for total package = sum of regional values
42
Experimental results
• 100% efficiency in nearly all cases
• Safe strategy adopted by bidders
– Clock stage
• Bid on most profitable package
– Supplementary round
• Bid full value on all relevant packages
– Assignment stage
• Bid incremental value for specific assignments
Conclusion
• Combinatorial clock auction
– Eliminates exposure
– Minimizes gaming
– Enhances substitution
– Allows auction to determine band plan
– Readily customized to a variety of settings
– Many other applications (airport slot auctions)
44
Incentive Auctions
45
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
46
Motivation
Year
Value per MHz
1985 1990 1995 2000 2005 2010 2015
Value of over-the-air broadcast TV
Value of mobile broadband
Gains from trade
48
Voluntary approach
TV broadcaster
freely decides to
Shar
e w
ith
an
oth
er
0 MHz 3 MHz 6 MHz
Spectrum freed
49
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
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
50
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
51
Market clearing and settlement
• 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
an
oth
er
0 MHz 3 MHz 6 MHz
Spectrum freed
Reverse auction to determine
supply
52
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
53
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
54
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
55
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
56
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
• Combinatorial clock auction ideal
– Within-region complementarities guaranteed with generic lots
– Across-region complementarities achieved with package bids
57
Forward auction to determine demand
Quantity
Price
P2
P3
P4
P5
P6 Supply
P0 P1
Demand
58
Forward auction to determine demand
Quantity
Price Supply
P*
Q* 59
Demand
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
60
Demand
Ways Congress can screw up (But they didn’t!!!)
• Impose restrictions on which broadcasters can participate in the auction – Destroys competition in reverse auction
• Make repacking purely voluntary – Creates holdout problem in reverse auction
– Reverses status quo—FCC can relocate stations
• Too greedy – Impose specific requirement on government
revenue share (e.g., Treasury gets 40% of revenue)
61
To Treasury
To TV broadcasters
Quantity
Price
Supply
PD
Q0
PS
Q*
Not too greedy: Quantity choice left to FCC
62
Demand
Quantity
Price
Supply
PD
Q40%
PS
Q*
Too greedy constraint: Treasury must get at least 40%
63
Demand To Treasury
To TV broadcasters
Revenue share constraint causes huge social welfare loss and reduces Treasury revenues!
Conclusion
• Efficient spectrum auctions can be done with modern methods
• Two-sided auctions can be effective to repurpose spectrum to more efficient use
64