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Auctions. What is an auction? Much broader than the “common-sense” definition. eBay is only one type of auction. An auction is a negotiation mechanism.

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Presentation on theme: "Auctions. What is an auction? Much broader than the “common-sense” definition. eBay is only one type of auction. An auction is a negotiation mechanism."— Presentation transcript:

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 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. $5 $3 $2 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. Homer Lisa/Bart OverbidsUnderbids No changeNo change or loss No change or overpay 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 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? Scheduling Example

27 Scheduling Example - solution Let’s start with afternoon Only agent 4 is interested, so he gets the four afternoon slots at reserve price (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 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” Scheduling Example - solution

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 = 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 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) Combinatorial auctions

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 Many billions of dollars at stake $22.9 B between 1994 and 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. Combinatorial auctions in real life

35 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 Combinatorial auctions in real life

36 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


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