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

– Exchanges are market/currency-based

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.

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?

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.

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.

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.

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.

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.

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.

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?

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

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.

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

• 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.

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.

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.

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

• 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• Highest bidder wins, but pays the second highest price.

It is a dominant strategy for each agent to bid his/heractual valuation.

$5 $3 $2

Homer wins and pays $3

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

Overbids Underbids

No change No change or loss

No changeNo change or overpay

Homer wins and pays $3

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.

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.

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

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.

• 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

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?

• 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

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.

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.

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.”

• 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

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.

• 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.

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 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

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

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.

Combinatorial auctions in real life

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