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The Exposure Problem in Static and Dynamic Auctions

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  • 1. The Exposure Problem in Static and Dynamic Auctions Wong Weng Yew, Joshua
  • 2. Introductions
  • 3. Economics is fun and motivating…
  • 4. nal number of licenses), the fifth the number of incumbents, the sixth the reve- nue per population unit, and the last the revenue divided by the population units per license, which is a more meaningful performance measure. and serious business… Table 1 UMTS Auctions in Europe in the Year 2000 Where When # Bidders # Licenses # Incumb !/Pop !/(Pop/Lic) UK 03/04 13 5 4 630 3150 Netherlands 07 9/6 5 5 170 850 Germany* 07/08 12/7 4-6* 4 615 3690 Italy 10 8/6 5 4 210 1050 Austria* 10 6 4-6* 3 103 618 Switzerland 11/12 10/4 4 3 19 76 UMTS Auctions in Europe in the Year 2000 Source: Grimm et al. (2003)
  • 5. Figure 1: European 2000-2001 3G Mobile Spectrum Auctions Per-Capita Revenues, by Country (right-hand scale) some interesting figures (auctions are shown on the dates at which they finished) Dow Jones European Telecom Stock Price Index (left-hand scale) 1700 700 1500 600 Revenue per Capita (Euros) 1300 500 Market Index (Euros) 1100 400 900 300 700 200 500 100 300 0 Netherlands Belgium Italy Germany Switzerland Austria Greece Denmark UK Jan-00 Jul-00 Jan-01 Jul-01 source: Klemperer
  • 6. beauty contests?
  • 7. Countries using auctions: Austria, Belgium, Denmark, Germany, Greece, Italy, Netherlands, Switzerland, UK Countries using beauty contests: Finland, France, Ireland, Norway, Portugal, Spain, Sweden beauty contests?
  • 8. Suppose you’re the Minister que ferais-tu?
  • 9. The Exposure Problem in Static and Dynamic Auctions 2 concerns – 2 problems – 2 auctions – 3 results
  • 10. Two concerns (in all auctions) Efficiency & revenue
  • 11. Why auctions? Efficiency: Auctions tend to put scarce resources in the hands of those who value them most Revenue: Higher revenues can displace distortionary tax revenues, and avoid giving firms big windfall gains for nothing
  • 12. Selling multiple objects Sellers are often interested in selling off a number of different objects: T-bills Mobile telephone licenses for different regions Procurement auctions (electric power generation) Collections (stamps, comic series) Logging rights on multiple parcels of land
  • 13. Two problems (in multi-unit auctions) Demand reduction & the exposure problem
  • 14. mpact the quantity demanded too. This reduces incentives to keep h. Demand reduction eme 1: Fixed demand Uniform price auction of carbon dioxide emissions reductions. bidding You are the big polluter, and you are bidding for promises to reduce emissions in return for true MC cash (supplying emission reductions). Say the price is now p, and there is excess supply. You can close the auction out by the amount of the excess supply Q and get the demanded units at the high price.
  • 15. Demand reduction Key take-away: Uniform pricing creates incentives for bidders to bid below their marginal values, creating inefficiencies.
  • 16. Demand reduction Key take-away: Uniform pricing creates incentives for bidders to bid below their marginal values, creating inefficiencies. Possible solutions: 1) reduce supply anti-competitively 2) create some elasticity 3) charge different prices for different units
  • 17. Exposure problem Complements + = Item A Item B AB Bidder 1 a b a+b+c Bidder 2 a + αc b + αc a+b
  • 18. Exposure problem Items may be complements, suggesting that prices of these items should be able to respond to each other. Selling two items, X and Y, sequentially: In bidding for X, bidders need to guess whether they can win Y. They might be too over-optimistic and only win one item. Alternatively, pessimistic bidders may fail to win when it is efficient for them to do so. Sell them in the same auction?
  • 19. Exposure problem Package bidding Bid withdrawals The FCC has been using an auction called the simultaneous ascending auction. Price discovery in the early rounds of the auction help bidders determine if winning their packages is feasible, which mitigates the exposure problem. However, Milgrom (2000)* shows that no competitive equilibrium exists nonetheless in the SAA when items are complements.
  • 20. Exposure problem Package bidding Bid withdrawals The FCC has been using an auction called the simultaneous ascending auction. Price discovery in the early rounds of the auction help bidders determine if winning their packages is feasible, which mitigates the exposure problem. However, Milgrom (2000)* shows that no competitive equilibrium exists nonetheless in the SAA when items are complements. Key takeaway: Bidders have to bid higher than their values for certain items in the package they want to win in order to have a chance of winning all items. They risk not winning all the items and thus overpaying for the items they won.
  • 21. There are some solutions Dasgupta and Maskin (2000) have proposed a “super” auction which is fully efficient, even with complementarity and I study two auctions which multiple units for sale. 1) are simple 2) have no demand reduction problem Unfortunately, the auction is too complicated to conduct in real life. I specifically analyze them in terms of their efficiency and revenue, and Combinatorial auctions can mitigate the bidder behaviour in response to the exposure problem. You bid only on exposure problem. packages you want. But this has its own problems (poor transparency, computational limits).
  • 22. Two auctions Vickrey & Ausubel
  • 23. Vickrey auction Recall: the uniform price auction is not efficient when multiple items are sold. Bidders submit price bids for each of the items. The auctioneer ranks the bids and the highest n bids win. However, bidders only pay the highest losing nth bids that they displace. It is a dominant strategy to just bid your values in this auction. Item A Item B Item C Bidder 1 12 11 10 Bidder 2 7 0 0 Bidder 3 9 7 6 Table 2: Bidder valuations Example: If all bidders bid according to the dominant strategy, then bidder 1 wins all three items and pays 3.2 Ausubel auction 9+7+7. This outcome is efficient. Analogous to the Vickrey auction is the auction proposed by Ausubel (2004). In this auction, the auctioneer, via the use of of an ascending clock, gradually increase prices, starting from
  • 24. Ausubel auction In this auction, the auctioneer names a price, and bidders make quantity bids at that price. Items, if any are won, are allocated at that price, and the auctioneer increases the price, prompting another bout of bidding. Bidders are not allowed to increase their quantity bids as the price increases, which allows for the following “clinching rule”: For each bidder, whenever the total bid of the other bidders is less than the supply, the bidder is deemed to have “clinched” the difference. It is an equilibrium strategy for bidders to bid for any item as long as their value for that item is more than the current price.
  • 25. Ausubel auction Brief Article Example: WongItem A Yew, Joshua C Weng Item B Item Bidder 1 12 11 10 Bidder 2 7 0 April 7, 2010 0 Bidder 3 9 7 6 Table 2: Bidder valuations Price Bidder 1 Bidder 2 Bidder 3 2 Ausubel auction 0 3 1 3 6 3 1 2 7 3 0 1 alogous to the Vickrey auction is the auction proposed by Ausubel (2004). In this auctio 9 3 0 0 auctioneer, via the use of of an ascending clock, gradually increase prices, starting fro ow price. At each posted price point, bidders make known the quantities that they wou e to be allocated. Allocation at each posted price is done by a simple procedure. For ea der, the residual supply, calculated by subtracting out from the total supply the sum of t
  • 26. Budget constraints • You are bidder 1 and you have $29 Item A Item B Item C • You donʼt know the Bidder 1 Bidder 2 12 7 11 0 10 0 values of the rest Bidder 3 9 7 6 • How do you bid? Table 2: Bidder valuations 3.2 Ausubel auction Analogous to the Vickrey auction is the auction proposed by Ausubel the auctioneer, via the use of of an ascending clock, gradually increa
  • 27. Experimental literature • Manelli et al. (2006) find similar efficiency in both auctions. • Engelmann and Grimm (2009) find overbidding in the Vickrey auction, less so in the Ausubel auction.
  • 28. Results On revenue, efficiency, and overbidding
  • 29. Experiments • Vickrey and Ausubel auctions • Items can be complements, or not • 3 items • 3 bidders
  • 30. Additive vs Complementary Environments • Additive environment: #!" • You simply add up the '#" values of the items you '!" won &#" • Complementary &!" environment: %#" • If you win one item, %!" thatʼs it. $#" • If you win two items, $!" add up the values, and #" multiply the sum by 1.5. • If you win three items, !" $"()*+" %"()*+," &"()*+," add up the values, and -..(/0*" multiply the sum by 2. 12+34*+*5)-67"
  • 31. would imply lower bidder surpluses in these auctions. In the complementary environm surpluses were similar in both auctions. Results The results seem to suggest that the Ausubel auction dominates the Vickrey auct of efficiency when items sold are complements. A discussion of the implications of is given in Section 6 on page 30. VAA (n = 7) AAA (n = 6) t-statistic (p-value) ranksu Efficiency 0.870 (0.181) 0.859 (0.184) 0.2362 (0.8176) Revenue 19.406 (4.876) 25.150 (4.969) −3.5289 (0.0047) Bidder surplus 5.737 (4.965) −0.267 (5.807) 3.0835 (0.0104) Conditional overbid 12.606 (10.994) 12.200 (11.325) 0.0964 (0.925) Conditional underbid 4.346 (4.688) 7.550 (7.714) −1.2669 (0.2314) Consistency 0.088 (0.107) 0.224 (0.188) −5.4236 (0.0002) VAC (n = 7) AAC (n = 6) t-statistic (p-value) ranksu Efficiency 0.488 (0.315) 0.772 (0.294) −4.8397 (0.0005) Revenue 27.477 (8.259) 32.492 (7.634) −1.5495 (0.1495) Bidder surplus 6.951 (10.416) 7.842 (9.798) −0.2456 (0.8105) Conditional overbid 35.776 (27.135) 33.158 (15.834) 0.2564 (0.8023) Conditional underbid 1.471 (2.332) 1.767 (3.196) −0.2771 (0.7868) Consistency 0.078 (0.131) 0.087 (0.132) −0.1959 (0.8483) Table 4: Summary of results. Means, standard deviationsstatistical methodology note on in parentheses, as well
  • 32. Revenue, additive • Revenue is higher in the Ausubel auction 30 beta = 0 Vickrey 28 Ausubel • Bidders bid higher than they should on their first few items 26 and lower on the rest 24 22 revenue 20 18 16 14 12 10 1 2 3 4 5 6 7 8 9 10 round
  • 33. Revenue, additive • Revenue is higher in the Ausubel auction 30 beta = 0 Vickrey 28 Ausubel • Bidders bid higher than they should on their first few items 26 and lower on the rest 24 22 • Bidder surplus is lower in revenue 20 Ausubel auction than Vickrey auction 18 16 14 12 10 1 2 3 4 5 6 7 8 9 10 round
  • 34. Revenue, additive • Revenue is higher in the Ausubel auction 30 beta = 0 Vickrey 28 Ausubel • Bidders bid higher than they should on their first few items 26 and lower on the rest 24 22 • Bidder surplus is lower in revenue 20 Ausubel auction than Vickrey auction 18 16 • Bidder surpluses are low in the 14 Ausubel auction 12 10 1 2 3 4 5 6 7 8 9 10 round
  • 35. Revenue, additive • Revenue is higher in the Ausubel auction 30 beta = 0 Vickrey 28 Ausubel • Bidders bid higher than they should on their first few items 26 and lower on the rest 24 22 • Bidder surplus is lower in revenue 20 Ausubel auction than Vickrey auction 18 16 • Bidder surpluses are low in the 14 Ausubel auction 12 • Learning? Revenues improve in 10 1 2 3 4 5 6 7 8 9 10 over 10 rounds in Vickrey. round Ausubel revenues are stable
  • 36. Revenue, complementary beta = 0.5 45 • Revenue is similar in both auctions 40 (statistically speaking). The graph suggests 35 revenue otherwise though: 30 • Learning? Revenues 25 improve in both Vickrey Ausubel auctions 20 1 2 3 4 5 6 7 8 9 10 round
  • 37. The index for consistency ranges from zero to one, the lower the in bidders (as defined on page 25). Efficiency, additive 5.2 Efficiency • Similar efficiencies In each round, the valuation of the allocation is given by adding 1 beta = 0 3 packages won by the individual bidders: V = j=1 vj . Given th • bidders in each round, it is possible to compute, using simple li 0.9 Rationality loss? 0.8 the 0.7 • Results possible the smallest similar to valued allocation and the optimal / highes 0.6 efficiency Vmin Manelli et ,al. (2006) three items are sold. In both auction m and Vmax where all 0.5 that this is precisely the case. Table 5 on the following page gives t 0.4 • Efficiency improved achievable in each round and for each bidding environment. We not 0.3 in the β =10 rounds in over 0.5 environment involve one person winning all three it 0.2 Vickrey Ausubel auction, not so 0.1 Ausubel in Vickrey auction 0 The index of efficiency in each round is given by 1 2 3 4 5 round 6 7 8 9 10 (dynamic learning?) V − Vmin Vmax − Vmin
  • 38. Efficiency, complementary • The Ausubel auction is 1 beta = 0.5 more efficient than the 0.9 Vickrey auction 0.8 0.7 • Exposure problem! 0.6 efficiency 0.5 • 0.4 Efficiency improved 0.3 over 10 rounds in 0.2 Ausubel auction, not 0.1 Vickrey Ausubel so in Vickrey auction 0 1 2 3 4 5 6 7 8 9 10 round (dynamic learning?)
  • 39. Exposure problem • In Ausubel auction, it is possible bid high with a low chance of making a loss Conversion of Ausubel quantity bids to (due to the price bids: complementarity condition) Same bids for all 3 items • In Vickrey auction, this is Vickrey Ausubel not possible Additive 3% 9% • Bidders feel more confident Complementary 8% 48% in bidding above their values if they have a lower chance of losing money • Bid data suggest this is the case
  • 40. Overbidding, additive beta = 0 50 • Overbidding does not 45 make sense in the 40 both auctions 35 Overbidding • 30 There is non-trivial 25 overbidding, similar in Vickrey 20 Ausubel both auctions 15 • 10 Overbidding is stable 1 2 3 4 5 6 7 8 9 10 round
  • 41. Overbidding, complementary • beta = 0.5 Difficulties in saying 50 what exactly is an 45 “overbid” due to the 40 complementarity 35 Overbidding condition 30 25 Vickrey • Ausubel Just a form of 20 comparison 15 10 • Not very useful 1 2 3 4 5 round 6 7 8 9 10
  • 42. Bidder surplus, additive beta = 0 18 16 Vickrey Ausubel 14 • Ausubel bidders earn 12 10 zero surplus biddersurplus 8 6 • Vickrey auction 4 2 favours bidders 0 −2 −4 1 2 3 4 5 6 7 8 9 10 round
  • 43. Bidder surplus, complementary beta = 0.5 18 Vickrey 16 Ausubel 14 • Similar bidder 12 surpluses 10 biddersurplus 8 • 6 But the Ausubel 4 auction is more 2 efficient 0 −2 −4 1 2 3 4 5 6 7 8 9 10 round
  • 44. Discussion For further research, thoughts
  • 45. Exposure problem revisited • Result is sensitive to • value distributions • number of bidders (more competitive) • “unequal” bidders • number of items • for sale • that bidders want • Intuitively, we should expect the exposure problem to be somewhat mitigated in the Ausubel auction, since the dynamic nature of the auction helps bidders form expectations of the final price they pay
  • 46. Overbidding • Are bidders rational? • Studies find overbidding in second-price sealed-bid single unit auctions • Not so for English (open ascending price) auctions • Dynamic nature helps bidders learn faster • BUT we find overbidding in both their multi-unit counterparts • Need more rounds for learning • Maybe bidders just like to win items? • An experiment with real monetary compensation could test for this (punishment for losing)
  • 47. Choice of auctions • Demand problem is not an issue in these auctions. Overbidding seems more prevalent than underbidding. • Simple to understand? Price discovery vs simplicity • These auctions can only sell very “similar” items • Other factors not considered in this auction are also very important: • Collusion (possible low revenues) • Perception of fairness and transparency
  • 48. Other topics of interest
  • 49. Problems encountered • Long duration • Logistical nightmare • Data consolidation • Participants uncertain about rules • Getting volunteers
  • 50. Experimental procedures
  • 51. Valuations • Valuations are drawn randomly for each item from the integers 0 to 10 inclusive. • The set of valuations for each session is exactly the same.
  • 52. Rules • Ausubel • The auction starts at price 5 and rises in increments of 0.5 • Vickrey • Bidders can bid prices anywhere from zero onwards, in multiples of 0.2 • All ties are randomly allocated
  • 53. Participants • Each participant played in total 20 rounds, in either the Vickrey or Ausubel auction. • Ten rounds in the additive environment • Ten rounds in the complementary environment
  • 54. Procedures • Instructional phase • Auction phase • Participants can ask questions at any time
  • 55. Miscellany
  • 56. vary demand according to Scheme 2: Variable demand price bidding true MC Q This is seldom seen in real life though. WHY? negative impact on Q back
  • 57. note on statistical methods • sample sizes are admittedly small • however, McCabe and Moore 1998 assert that the two-sample t-test is quite accurate for a broad range of distributions when the sample sizes are as small as 5 • the test is robust to small sample sizes (Posten 1978) • a similar study (Manelli et al. 2006) used sample sizes of 5 and 4. back
  • 58. Package bidding • More efficient as complementarity increases • Longer to complete • Lower revenues back
  • 59. Bid withdrawals • Porter (1999) • Efficiency and revenue do increase, but at expense of bidder surpluses back