Auctions

1. Auctions

2. What is an auction? • Much broader than the “common-sense” definition. • eBay is only one type of auction. • An auction is a negotiation mechanism where: • The mechanism is well-specified (it runs according to explicit rules) • The negotiation is mediated by an intermediary • Exchanges are market/currency-based

3. Mediation • In a traditional auction, the mediator is the auctioneer. • Manages communication and information exchange between participants. • Provides structure and enforcement of rules. • The mediator is not an agent or a participant in the negotiation. • Think of it as an automated set of rules.

4. Types of auctions • Open vs sealed-bid • Do you know what other participants are bidding? • One-sided vs. two-sided • Do buyers and sellers both submit bids, or just buyers? • Clearing policy • When are winners determined (occasionally, continuously, once?) • Number of bids allowed • One, many?

5. Some classic auction types • English outcry auction • This is the auction most people are familiar with. • One-sided (only buyers bid) • Bids are publicly known • Variant: only highest bid is known. • Bids must be increasing • Auction closes when only one bidder is left.

6. Some classic auction types • Dutch outcry auction • Used to sell tulips in Dutch flower markets. • Closes quickly. • One-sided (only buyers bid) • Bids are publicly known • Bids must be decreasing • Auctioneer starts at max, lowers asking price until someone accepts. • Auction closes when anyone accepts.

7. Some classic auction types • Vickrey auction. • One-sided (only buyers bid) • Bids are publicly known • Turns out not to matter whether bids are secret. • Highest bid receives the good, pays second-highest bid. • Has the nice property that truth-telling (bidding your actual valuation) is a dominant strategy.

8. Some classic auction types • First-price sealed-bid • This is how houses, construction bids, etc are sold. • One-sided (only buyers bid) • Bids are hidden; each buyer bids in secret. • Everyone bids once. • Highest (or lowest) bidder wins. • Bidder challenge: guessing the bids of other buyers.

9. Some classic auction types • Continuous double auction • This is NASDAQ, NYSE, etc work • Two-sided: Sellers and buyers both bid • Matches are made continuously • Matches are made based on the difference between the “bid” price (willingness to pay) and the “ask” price (amount seller wants) • Bidder challenge: guessing future movement of clearing prices.

10. Auction (mechanism) properties • When choosing an auction type, one might want: • Efficiency • Agents with the highest valuations get the goods. • If not, expect an aftermarket to develop. • Incentive Compatibility • The optimal strategy is to bid honestly • Easy for participants – no need to counterspeculate • Easy to determine the efficient allocation.

11. Auction (mechanism) properties • How is surplus distributed? • Which consumers are happiest? • Who pays transaction costs? How much are they? • Can the mechanism be manipulated by coalitions? • How long does it take to close? • Can is be guaranteed to close in finite time?

12. Valuation of goods • Items to be auctioned can be: • Private value/independent value • The amount a person is willing to pay does not depend upon how much others will pay. • Item will be consumed/used rather than resold • Electricity, computational resources, food • Common value • The amount a person is willing to pay depends upon the value others place on the good • Item is bought as an investment • Stock, gold, antiques, art, oil prospecting rights

13. Valuation of Goods • Items to be auctioned can be: • Correlated value • Some private valuation and some common value • Item may have network effects – e.g. VCRs, computers. • Item may provide both value and investment – some artwork or collectibles. • Challenge with correlated/common value goods: Estimating what others will pay.

14. The Winner’s Curse • Correlated and common-value auctions can lead to a paradox known as the Winner’s Curse. • In a first-price auction, the winner knows that he/she paid too much as soon as the auction is over. • No one else would buy at that price. • Assumption: everyone has the same information. • Applicable to prospecting, buying companies, signing free agents, investing in artwork, etc.

15. English Auctions • These are the most common auctions in practice. • Bids ascend, winner gets the item at the price she bid. • Optimal strategy, bid $0.01 more than the next highest person.

16. English Auctions • In an open outcry auction, this is easy. • Just keep going until no one else is bidding. • For the seller to be happy, there must be enough competition to drive up bids. • Open outcry can also reveal information to others. • This may be a problem. • Can also encourage collusion • Bidders agree to keep prices low, possibly reselling later.

17. English Auctions • In sealed-bid auctions, selecting a bid price is a serious problem. • Need to guess what others will bid, and what they think you will bid, etc. • Problem: item may not actually go to the bidder who values it most.

18. Dutch auctions • Start at max, auctioneer gradually decreases bid. • Strategy: bid $0.01 above what the next highest person is willing to pay. • Equivalent in terms of revenue to a first-price auction. • Has the advantage of closing quickly.

19. Vickrey auctions • In a Vickrey auction, the highest bid wins, but pays the second-highest price. • If goods are privately valued, it is a dominant strategy for each participant to bid their actual valuation. • Prevents needless and expensive counterspeculation • Ensures that goods go to those who value them most.

20. $3 $2 $5 Example: Vickrey auction • Highest bidder wins, but pays the second highest price. It is a dominant strategy for each agent to bid his/her actual valuation. Homer wins and pays $3

21. Example: Vickrey auction • Highest bidder wins, but pays the second highest price. Homer: $5, Bart $3, Lisa $2 It is a dominant strategy for each agent to bid his/her actual valuation. Overbids Underbids No change No change or loss Homer No change or overpay Lisa/Bart No change Homer wins and pays $3

22. Using Auctions for Scheduling • Auctions can be used for lots more than just buying beanie babies on eBay. • A new and popular approach is to use auctions for allocation of resources in a distributed system. • Electric power in Sweden • Computational resources (disk, CPU, bandwidth) • This approach is called market-oriented programming.

23. Market-oriented scheduling • Appeal: if assumptions are met, we can find the optimal schedule. • Participants in the system have no incentive to misrepresent the importance of their job. • Much of the computation is decentralized • Since scheduling is often NP-complete, we’d like to avoid having a single process find a solution.

24. Scheduling example • Consider a schedule with 8 1-hour slots from 8am to 4 pm • Each slot has a reserve price = $3 • This is the cost needed to run the machine for an hour. • Bids must meet or exceed reserve. • 4 agents have jobs to submit. • Agent 1: 2 hours (consec.), value $10, deadline: noon • Agent 2: 2 hours (consec), value $16, deadline: 11am • Agent 3: 1 hour, value $6, deadline 11 am. • Agent 4: 4 hours (consec), value $14.5, deadline 4pm

25. Scheduling Example • We cannot satisfy all agents • 9 hours needed in an 8 hour day. • We would like to schedule the most valuable jobs. • We need to accurately know which jobs are the most valuable. • Everyone thinks their job is the most important. • This is the same as maximizing revenue in an auction.

26. Scheduling Example • We use a Vickrey auction to allocate slots. • Each agent will bid their actual valuation for the slots. • No incentive to counterspeculate. • Agent 1 will bid $10 for any two slots before noon. • Agent 2 will bid $16 for any two slots before 11 am. • Agent 3 will bid $6 for any one slot before 11am. • Agent 4 will bid $14.50 for any four slots. • So what is the solution?

27. Scheduling Example - solution • Let’s start with afternoon • Only agent 4 is interested, so he gets the four afternoon slots at reserve price + 0.25 (minimum bid) • Gets slots for $13, which is less than the value of the job, so he’s happy. • Morning • Agent 1 bids $16 for two slots ($8 per) – no one else can beat this, so he’ll get two slots (8am & 9am) at the second price. • But what is the second price?

28. Scheduling Example - solution • Agent 2’s bid: • price(s1) + price(s2) = 10, price(s2) >= $3.25 • Since no one else wants s2, agent 2 can have s2 for $3.25. This means his bid for s1 is $6.75 • Agent 3 bids $6 for s1 • We now have 3 resources and 4 bids. • The first three slots are allocated at $6.25 apiece, and the remainder at $3.25 • This is an equilibrium • At these prices, no one wants to change their allocation. • The most valuable jobs are scheduled – we’ve maximized global performance. • Each agent had no incentive to “cheat the system”

29. Double Auctions • In a double auction, both buyers and sellers select bids. • Most often, these auctions are continuous • Any time there is a possible match, it is made. • The NYSE, NASDAQ, most futures markets work this way.

30. Double Auctions • Prices are represented as a bid/ask spread • This is the highest unmet bid to buy, and the lowest unmet bid to sell. • Example: • buy: 34, 36, 40, 47, 48 • sell: 50,52, 55, 60 • Bid/ask spread = 48-50 • Any “buy” greater than 50, or any sell less than 48 will close immediately. • In theory, the market will converge to an equilibrium.

31. Combinatorial auctions • In all the problems we’ve seen so far, a single good is being sold. • Often, a seller would like to sell multiple interrelated goods. • FCC spectrum is the classic example. • Bidders would like to bid on combinations of items. • “I want item A, but only if I also win the auction for item B.”

32. Combinatorial auctions • If we sell each good in a separate auction, agents have a hard bidding problem. • I don’t want to win only A, so I need to estimate my chances of winning B. • We might also let people place bids on combinations of goods. • Problem: determining the winner is NP-hard. • Determining what to bid is at least that hard. • Compromise: allow restricted combinations of bids. (e.g. only XOR)

33. Combinatorial auctions in real life • In 1994, the FCC began auctioning of license for portions of the EM spectrum • Cellphone coverage, radio and television, wireless communication, etc. • Large complementarities exist. • A given frequency in San Francisco is more valuable if Cingular also has the same frequency in Los Angeles.

34. Combinatorial auctions in real life • Many billions of dollars at stake • $22.9 B between 1994 and 1998. • Companies have a large incentive to “cheat” • FCC would (in theory) like to maximize revenue and efficiency. • Can’t actually do both • Values are correlated • Firms have their own interest, plus a concern for the “market value” of a particular region.

35. Combinatorial auctions in real life • The FCC conducted a series of simultaneous multiple-round open single-good auctions. • Too complex to auction everything at once. • Still want bidders to get efficient combinations. • Helps bidders determine how valuable a license is. • Bidders could withdraw • Allowed them to try to get complementary frequencies without undue risk

36. Combinatorial auctions in real life • Problems • Collusion – bidders would buy arbitrarily, move across the street, and reallocate. • Code bidding. Bidders would use bids to indicate to competitors which markets they wanted. • Sprint wants a freqency in Northern Ca (zone 37) • Cingular really needs a certain frequency in NYC • When Cingular starts bidding up the price in Northern CA, Sprint submits a high bid in NYC: $24,000,000,037 • The message: if you stay in zone 37, we’ll bid up the price here. • Expensive NYC bid then withdrawn by Sprint

37. Combinatorial auctions in real life • Code bidding also used to signal markets a buyer particularly wants. • Bid in a rival’s market; when they back out of yours, withdraw. • Solution: hide identity of bidders • Bidders used telephone keypad numbers to identify themselves. • TDS ended bids in 837

38. Combinatorial auctions in real life • FCC responses • Click-box bidding. Bidder chooses a market, their bid is one increment more than highest. • Limit the number of withdrawals • Only two rounds allowed. • Set high reserve prices • Less temptation to collude • Encourage small-firm competition • Provide credits/assistance to smaller businesses • More competition means less collusion • Stagger closing times • Once an auction has closed ,the winner is safe from retaliatory bidding.

39. Summary • There are a great variety of auction types • Features can be selected to achieve the desired outcomes. • In private-value auctions, a Vickrey auction has the desirable property of incentive compatibility. • This makes it attractive for scheduling and resource allocation in CS problems • Combinatorial auctions present a new suite of challenges • Complementarity, collusion, tractability. • Auctions are one of the “hottest” research topics