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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 where: The mechanism is well-specified (it runs according to explicit rules) The negotiation is mediated by an intermediary

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Auctions l.jpg

Auctions


What is an auction l.jpg

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


Mediation l.jpg

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.


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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?


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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.


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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.


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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.


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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.


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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.


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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.


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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?


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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


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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.


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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.


English auctions l.jpg

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.


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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.


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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.


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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.


Vickrey auctions l.jpg

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.


Example vickrey auction l.jpg

$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


Example vickrey auction21 l.jpg

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


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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.


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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.


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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


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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.


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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?


Scheduling example solution l.jpg

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?


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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”


Double auctions l.jpg

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.


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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.


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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.”


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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)


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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.


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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.


Slide35 l.jpg

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


Combinatorial auctions in real life36 l.jpg

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


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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


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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.


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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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