Spectrum Auction Design

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1 Spectrum Auction Design Peter Cramton Professor of Economics, University of Maryland 1

2 Two parts One-sided auctions Two-sided auctions (incentive auctions)

3 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

4 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

5 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

6 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

7 Rigid band plans: something for everyone US AWS band plan: something for everyone Uplink A B C D E F Bandwidth MHz MHz 1 MHz 1 MHz 1 MHz MHz Partition Small Medium Medium Large Large Large Regions Downlink A B C D E F

8 Day 3 8 A B C D E AWS price for 1 MHz by block 734 CMAs 17 EAs REAGs F A Day 4 1 B C D E F A B Day 1 C D E F A B Stage 31 C D E F Final 11 A B C D 4% discount E F M 1M M 3M 4M M M 7M 8M 9M 1M 11M 1M 13M 14M 1M 1M 17M 18M 19M M 1M High Bids per 1 MHz Sum of pwb amount per 1 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, 1, 1, 31 and 11. license_size_mhz 1

9 Limited substitution: 7 MHz MHz, 1 rounds, $19. billion Block A B C Bandwidth 1 MHz 1 MHz MHz Type paired paired paired Partition Price $1.1 $.8 $.7 Verizon AT&T Verizon and AT&T won 8% of spectrum

10 German 4G Auction: 3 MHz, 4 rounds, 4.4 billion 8 Winner A B C D E F T-Mobile Vodafone O E-plus Final bid 1,9 9,7 7,849 8,949 83, 7, Winner A B C x MHz D x17.4 MHz x.4 MHz E Final bid,7,7 19,89 1, 1,3 x17.4 MHz. Winner E TDD MHz TDD MHz TDD MHz TDD x1 MHz A B C D Final bid,731 93,77 13,33 84,4,931 x1 MHz x1 MHz x1 MHz F TDD,71. Winner A B C D E F G H I J K L M N Final bid 19,9 19, 17,34 17,34 18,948 19, 19,9 19,38 18,948 18,931 17,739 17,739 17,739 17,7. Winner O P Q R S T U V W X TDD Final bid 9,13 9,13 8,98 8,98 9,1 9,1 8,73 8,9 8,9 8,9 Average Price in Each Band ( /MHz-pop) 8 MHz 1.8 GHz. GHz. GHz. GHz E. GHz F. GHz TDD

11 German 4G auction key features Full transparency Low reserve prices Bidders clearly signaled outcome in 1 st round Only conflict was E-plus 1 lot at 8 MHz Auction conducted on-site with 198 software that failed after the first round 11

12 Italy 4G Auction, Final Outcome Round rounds, days, 3.9B Total bid Total winning 8 MHz 1,8 MHz Number of lots won, GHz, MHz TDD, MHz TDD 8 MHz Price (euro) per MHz-Pop, 1,8, MHz MHz GHz TDD submitted bid W 1, ,119.9 (s) 4 (s).81.9 T 1,.3 1, V 1,9.8 1, H Players No bids, MHz TDD 8 MHz 8_S 8G 8G 8G 8G 8G ,8 MHz 18G 18G 18G , MHz A 77.93, MHz FDD G G G G G G G G G G G _S , MHz TDD B C

13 Italy 4G Auction Key features Full transparency Ranking list for each category (provisional winners) No activity rule 8 closes after 3 rounds without bids in any category Auction closes after rounds without any bids in any category Makes this a sequential auction: 8 then other bands, since 8 must close first Auction conducted on-site with pen and paper 13

14 Combinatorial Clock Auction 14

15 Needed enhancements Anonymous bidding Generic lots Package bidding with clock Porter-Rassenti-Roopnarine-Smith (3) Ausubel-Cramton (4) Ausubel-Cramton-Milgrom () Second pricing Revealed preference activity rule

16 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 1

17 UK spectrum auctions

18 UK auctions 1-4 GHz: fixed wireless or backhaul L-Band: mobile broadcast. GHz: 4G mobile wireless (13) Digital Dividend: 4G, mobile TV, DTT (13) Requirements Technology neutral Flexible spectrum usage rights Efficient assignment

19 UK. GHz auction 19 MHz (38 lots of MHz) How much paired vs. unpaired? CEPT band plan from Electronic Communications Committee Decision () Type Lot Frequency Paired (FDD uplink) Paired (FDD downlink) Unpaired (TDD)

20 Let auction determine band plan Increase in unpaired spectrum maintaining 1 MHz duplex spacing Type Lot Frequency All unpaired spectrum Type Lot Frequency Unpaired (TDD) Unpaired Paired (FDD uplink) Unpaired (TDD) Paired (FDD downlink)

21 Key design choices Generic 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

22 Pricing rule

23 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

24 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 4

25 Optimization Core point that minimizes payments readily calculated Solve Winner Determination Problem Find Vickrey prices Constraint generation method (Day and Raghavan 7) Find most violated core constraint and add it Continue until no violation Tie-breaking rule for prices is important Minimize distance from Vickrey prices

26 bidder example with bids on {A,B} b 1 {A} = 8 b {B} = b 3 {AB} = 3 b 4 {A} = 14 b {B} = 1 Winners Vickrey prices: p 1 = 14 p = 1

27 The Core Bidder Payment b 3 {AB} = 3 b 4 {A} = 14 b 1 {A} = 8 Efficient outcome b {B} = The Core 1 b {B} = Bidder 1 Payment 7

28 Vickrey prices: How much can each winner s bid be reduced holding others fixed? Bidder Payment b 3 {AB} = 3 b 4 {A} = 14 b 1 {A} = 8 b {B} = The Core 1 Vickrey prices Problem: Bidder 3 can offer seller more (3 > )! b {B} = Bidder 1 Payment 8

29 Bidder-optimal core prices: Jointly reduce winning bids as much as possible Bidder Payment b 3 {AB} = 3 b 4 {A} = 14 b 1 {A} = 8 b {B} = The Core 1 Vickrey prices Problem: bidderoptimal core prices are not unique! b {B} = Bidder 1 Payment 9

30 Core point closest to Vickrey prices Bidder Payment b 3 {AB} = 3 b 4 {A} = 14 b 1 {A} = 8 b {B} = 1 Unique core prices 1 Vickrey prices Each pays equal share above Vickrey b {B} = Bidder 1 Payment 3

31 Activity rule 31

32 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 1 to at prices p For all packages q of size 7 to 1, bid q p Implication Profit maximization is poor strategy Bid to maximize package size subject to profit

33 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 = $4 Realistic scenarios

34 Result Activity rule causes major deviation from straightforward bidding Undermines price discovery Reduces efficiency

35 Activity rule readily fixed: Revealed preference At time t > t, package q t has become relatively cheaper than q t (P ) q t (p t p t ) q t (p t p t ) 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

36 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 Marginal Value Average Value Bidder A Bidder B Bidder A Bidder B 1 lot lots 9 Each wins one; price = Competitive equilibrium! A wins both; price = 8 Too concentrated; too high priced!

37 Demand downward sloping Average value > marginal value Price Supply Eligibility point price Average Value Revealed preference price = Competitive equilibrium price Marginal Value Quantity

38 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 q f b( q) b( q ) ( q q ) p f f f Packages q larger than q f 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 38

39 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

40 Properties with substitutes Bidding on most profitable package is best Clock yields competitive equilibrium with efficient assignment and supporting prices Final assignment = clock assignment 4

41 Properties in general Supplementary bids needed To identify efficient assignment To determine competitive prices 41

42 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 4

43 Experimental results 1% 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

44 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

45 Incentive Auctions 4

46 Incentive auctions Low value Over-the-air TV broadcast High value Mobile broadband Auction includes essential regulatory steps to address market failures in the secondary market for spectrum 4

47 Letter from 11 economists, April 11 47

48 Value per MHz Motivation Value of mobile broadband Value of over-the-air broadcast TV Gains from trade Year 48

49 Share with another Voluntary approach TV broadcaster freely decides to For simplicity, I assume that channel sharing is only :1; other possibilities could also be considered, including negotiated shares with particular partners announced at qualification Spectrum freed MHz 3 MHz MHz 49

50 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

51 Two approaches Combinatorial exchange Too complex due to repacking Reverse auction to determine supply Optimization gives mandatory repacking options Forward auction to determine demand Market clearing and settlement 1

52 Share with another TV broadcaster freely decides to Spectrum freed Reverse auction to determine supply MHz 3 MHz MHz Mostly single channel Price discovery less important => Sealed-bid auction or descending clock Price to cease Price to share

53 Washington DC MHz 3 MHz MHz P = $3 7 Price = $3/MHzPop Reverse auction to determine supply S =

54 Washington DC MHz 3 MHz MHz P = $ 7 Price = $/MHzPop Reverse auction to determine supply S =

55 Washington DC MHz 3 MHz MHz P = $1 7 Price = $1/MHzPop Reverse auction to determine supply S =

56 P = $ Supply = S = 3 1 MHz Mandatory repacking

57 Forward auction to determine demand Mobile operators want large blocks of contiguous paired spectrum for LTE (4G) One to four 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 7

58 Price P Supply P Forward auction to determine demand P 4 P 3 P P 1 Demand Quantity 8

59 Price Supply Forward auction to determine demand P* Demand Q* Quantity 9

60 Price Supply Forward auction to determine demand 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 P D P S To Treasury To TV broadcasters Q Q* Demand Quantity

61 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 4% of revenue) 1

62 Price Not too greedy: Quantity choice left to FCC Supply P D P S To Treasury To TV broadcasters Demand Q Q* Quantity

63 Price Too greedy constraint: Treasury must get at least 4% Revenue share constraint causes huge social welfare loss and reduces Treasury revenues! Supply P D To Treasury P S Demand To TV broadcasters Q 4% Q* Quantity 3

64 Conclusion Efficient spectrum auctions can be done with modern methods Two-sided auctions can be effective to repurpose spectrum to more efficient use 4