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