About the type of auction by Allan Baitcher

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Auctions

• Allan Baitcher

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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

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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 Winners Curse

• Correlated and common-value auctions can lead to
  a paradox known as the Winners 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.

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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.

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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.

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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
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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, wed 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?

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Scheduling Example - solution

• Lets 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 hes happy.
• Morning
• Agent 1 bids 16 for two slots (8 per) no one
  else can beat this, so hell get two slots (8am
  9am) at the second price.
• But what is the second price?

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Scheduling Example - solution

• Agent 2s bid
• price(s1) price(s2) 10, price(s2) gt 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 weve
  maximized global performance.
• Each agent had no incentive to cheat the system

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• THANK YOU