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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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what is an auction
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
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
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
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 types6
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 types7
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 types8
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 types9
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
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 properties11
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
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 goods13
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
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
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 auctions16
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 auctions17
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
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
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

$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
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

using auctions for scheduling
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
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
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 example25
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.
slide26

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
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?
slide28

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
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 auctions30
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
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.”
slide32

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
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.
slide34

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

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
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 life37
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 life38
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
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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