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OverviewOverview
General review of common auctionsGeneral review of common auctions Auction design for agents with hard Auction design for agents with hard
valuation problemsvaluation problems Auction design for goods in Auction design for goods in
unlimited supplyunlimited supply
Auction DesignAuction Design
Many different protocolsMany different protocols Major auction types:Major auction types:
Ascending Price (English)Ascending Price (English) Descending Price (Dutch)Descending Price (Dutch) First Price, Sealed BidFirst Price, Sealed Bid Second Price, Sealed Bid (Vickrey)Second Price, Sealed Bid (Vickrey)
Essentially mixing and matching Essentially mixing and matching certain properties, but some certain properties, but some combinations work better than otherscombinations work better than others
Auction EvaluationAuction Evaluation
Revenue for the sellersRevenue for the sellers Profit for the biddersProfit for the bidders Avoidance of “winner’s curse” helps Avoidance of “winner’s curse” helps
bothboth Winner in most auction protocols is the Winner in most auction protocols is the
participant who made the biggest participant who made the biggest overvaluation mistakeovervaluation mistake
Auctions that decouple an agent’s bid from Auctions that decouple an agent’s bid from the actual price paid encourage higher the actual price paid encourage higher bidsbids
Ascending Price Ascending Price (English)(English)
Most commonly known protocolMost commonly known protocol Auctioneer starts with an opening Auctioneer starts with an opening
bid and successively raises the price bid and successively raises the price as participants are willingas participants are willing
Allows for dynamic adjustment of Allows for dynamic adjustment of bidders’ valuations by giving bidders’ valuations by giving information about other biddersinformation about other bidders
Buyers bid at most their utility, Buyers bid at most their utility, which may be adjusted on the flywhich may be adjusted on the fly
Descending Price Descending Price (Dutch)(Dutch)
Biddings starts at an extremely high Biddings starts at an extremely high price and descends until someone price and descends until someone claims the itemclaims the item
High degree of Winner’s CurseHigh degree of Winner’s Curse Intuitively, raises seller’s revenue in Intuitively, raises seller’s revenue in
cases when the high bidder wants an cases when the high bidder wants an item badlyitem badly
First Price, Sealed BidFirst Price, Sealed Bid
Buyers submit bids onceBuyers submit bids once No knowledge of one another’s bidsNo knowledge of one another’s bids Auctioneer opens bids and sells the Auctioneer opens bids and sells the
item to the highest bidder at the price item to the highest bidder at the price he submittedhe submitted
Encourages buyers to bid Encourages buyers to bid conservatively (shade down from conservatively (shade down from utility) to maximize profit versus utility) to maximize profit versus probability of winningprobability of winning
Second Price, Sealed Bid Second Price, Sealed Bid (Vickrey)(Vickrey)
Designed to alleviate Winner’s Curse Designed to alleviate Winner’s Curse in the First Price, Sealed Bid protocolin the First Price, Sealed Bid protocol
Same sealed bid format, but item is Same sealed bid format, but item is awarded to the highest bidder at the awarded to the highest bidder at the second highest pricesecond highest price
Buyers can bid their utility to increase Buyers can bid their utility to increase probability of winning, but are probability of winning, but are guaranteed a price closer to market guaranteed a price closer to market consensusconsensus
Optimal Auction Design for Optimal Auction Design for Agents with Hard Valuation Agents with Hard Valuation
ProblemsProblemsDavid C ParkesDavid C Parkes
MotivationMotivation Standard auction theory assumes that Standard auction theory assumes that
either agents know own their utility for either agents know own their utility for an item (private value) or that there is a an item (private value) or that there is a common utility that is unknown to the common utility that is unknown to the agents (common value)agents (common value)
As transactions are increasingly turned As transactions are increasingly turned over to software agents, the cost of over to software agents, the cost of obtaining this utility value may be obtaining this utility value may be significantsignificant
Certain auction designs can simplify this Certain auction designs can simplify this problemproblem
Paper GoalsPaper Goals
Compare the performance of agents Compare the performance of agents with hard valuation problems within with hard valuation problems within three auction designsthree auction designs Posted Price, sequentialPosted Price, sequential Second Price, sealed bidSecond Price, sealed bid Ascending PriceAscending Price
What the paper isn’t about: Actual What the paper isn’t about: Actual methods for refining beliefs about methods for refining beliefs about valuesvalues
Examples of Hard Examples of Hard ValuationValuation
Agents bidding for components on Agents bidding for components on behalf of a manufacturerbehalf of a manufacturer
Agents bidding for collectibles or Agents bidding for collectibles or other raritiesother rarities
Problem FormulationProblem Formulation
Agents with hard valuation problems Agents with hard valuation problems operate in three phases:operate in three phases: Metadeliberation: Decide how much Metadeliberation: Decide how much
effort to spend refining the valuation of effort to spend refining the valuation of the itemthe item
Valuation: The refinement process – Valuation: The refinement process – solve an optimization problem, interact solve an optimization problem, interact with a human expert, etcwith a human expert, etc
BiddingBidding
Agent ModelAgent Model Each agent has an unknown true value Each agent has an unknown true value
for an itemfor an item Each agent maintains an upper and Each agent maintains an upper and
lower bound, in which the true value is lower bound, in which the true value is assumed to be somewhere, uniformly assumed to be somewhere, uniformly distributed, in betweendistributed, in between
Expected true value is then the Expected true value is then the average of the upper and lower boundsaverage of the upper and lower bounds
The deliberation process refines the The deliberation process refines the upper and lower boundsupper and lower bounds
Agent ModelAgent Model
Deliberation
Incurs cost C
Upper Bound
Lower Bound
New Upper Bound
New Lower Bound
Expected True Value
New ExpectedTrue Value
ParametersParameters
Cost of Deliberation (C)Cost of Deliberation (C) Computational Effectiveness of Computational Effectiveness of
Deliberation (1-Deliberation (1-))
MetadeliberationMetadeliberation
Solve the tradeoff between reducing Solve the tradeoff between reducing uncertainty and incurring the cost of uncertainty and incurring the cost of deliberationdeliberation
Deliberation is only worthwhile when:Deliberation is only worthwhile when: It changes the agent’s bidIt changes the agent’s bid The new bid has a greater expected The new bid has a greater expected
utility than the old bidutility than the old bid Metadeliberation strategies vary by Metadeliberation strategies vary by
auction typeauction type
Metadeliberation StrategiesMetadeliberation StrategiesVickrey AuctionVickrey Auction
Need distributional information about the bids Need distributional information about the bids of other agentsof other agents
Paper assumes such information is somehow Paper assumes such information is somehow obtained by the agents (eg learning)obtained by the agents (eg learning)
Metadeliberation strategy:Metadeliberation strategy: Deliberate until utility of placing a bid now is Deliberate until utility of placing a bid now is
greater than the estimated utility of placing a bid greater than the estimated utility of placing a bid after another deliberation stepafter another deliberation step
Bid utility is a nonlinear function of expected valueBid utility is a nonlinear function of expected value Higher bid decreases profit but raises probability of Higher bid decreases profit but raises probability of
winningwinning
Metadeliberation StrategiesMetadeliberation StrategiesVickrey AuctionVickrey Auction
Length of time that an agent spends Length of time that an agent spends deliberating depends on:deliberating depends on: The number of agents in the auctionThe number of agents in the auction The agent’s current upper and lower The agent’s current upper and lower
bounds on the value of the item bounds on the value of the item The computational effectiveness of The computational effectiveness of
deliberation (1-deliberation (1-)) The cost of deliberation (C)The cost of deliberation (C)
Metadeliberation StrategiesMetadeliberation StrategiesPosted Price SequentialPosted Price Sequential
No uncertainty about the actions of No uncertainty about the actions of other agentsother agents
Need only to worry about the cost of Need only to worry about the cost of the goodthe good
Deliberate only when the ask price is Deliberate only when the ask price is within the bounds of some threshold within the bounds of some threshold function function ((, C, , C, ))*
Accept Price
Deliberate
Reject Pricev
v
Metadeliberation StrategyMetadeliberation StrategyAscending PriceAscending Price
Third action available in addition to Third action available in addition to bid and deliberate: waitbid and deliberate: wait Agents that wait benefit from the Agents that wait benefit from the
deliberation of othersdeliberation of others Optimal Strategy:Optimal Strategy:
Bid
Wait, or Deliberate if auction will close, with probability 1/(Na -1)
Leave auctionv
v
Evaluation MetricsEvaluation Metrics Efficiency:Efficiency:
True Value for the Good for the Winning True Value for the Good for the Winning Agent / Maximum True Value over All Agent / Maximum True Value over All AgentsAgents
Revenue:Revenue:Price Paid for the Good / Maximum True Price Paid for the Good / Maximum True Value over All AgentsValue over All Agents
Utility of Participation:Utility of Participation:(Surplus to Winning Agent – Total (Surplus to Winning Agent – Total Deliberation Cost for All Agents) / Deliberation Cost for All Agents) / Number of AgentsNumber of Agents
Evaluation ArmsEvaluation Arms
Variance of:Variance of: Number of AgentsNumber of Agents Computational Effectiveness (1-Computational Effectiveness (1-)) Cost of Deliberation (C)Cost of Deliberation (C) Agent “experience” – Adjust C and Agent “experience” – Adjust C and for for
fractions of the agent populationfractions of the agent population
Varying the Number of Varying the Number of AgentsAgents
+ Ascending Price
X Sealed Bid
O Posted Price Sequential
Varying the Computational Varying the Computational Effectiveness of Effectiveness of
DeliberationDeliberation
+ Ascending Price
X Sealed Bid
O Posted Price Sequential
Varying Agent Varying Agent ExperienceExperience
+ Ascending Price
X Sealed Bid
O Posted Price Sequential
Competitive Auctions and Competitive Auctions and Digital GoodsDigital Goods
Andrew GoldbergAndrew Goldberg
Jason D HartlineJason D Hartline
Andrew WrightAndrew Wright
MotivationMotivation Looking for an optimal way to sell goods Looking for an optimal way to sell goods
in unlimited supplyin unlimited supply Downloadable musicDownloadable music Pay per view moviesPay per view movies
Examines auctions as an alternative to Examines auctions as an alternative to fixed pricing, which requires expensive fixed pricing, which requires expensive and probably inaccurate market researchand probably inaccurate market research
Scary implication: Charge more for Scary implication: Charge more for media created by entities with small, media created by entities with small, rabid followings?rabid followings?
The Optimal Threshold The Optimal Threshold FunctionFunction
Given a set of bids, determine the Given a set of bids, determine the single price that maximizes revenuesingle price that maximizes revenue
3 3 3 2 2 1
• 3 at 3 (9)• 5 at 2 (10)• 6 at 1 (6)
Sell…
Paper GoalsPaper Goals
Examine classes of single round, Examine classes of single round, sealed bid auctions for products with sealed bid auctions for products with no marginal cost of reproductionno marginal cost of reproduction
Need to solve tradeoff between selling Need to solve tradeoff between selling a lot at a low price versus a few at a a lot at a low price versus a few at a high pricehigh price
Need to ensure that participants bid Need to ensure that participants bid their utilitiestheir utilities
Would like an auction mechanism that Would like an auction mechanism that compares well to optimal fixed pricingcompares well to optimal fixed pricing
TerminologyTerminology
Truthful auctionsTruthful auctions Encourage participants to bid their utilityEncourage participants to bid their utility More formally: More formally:
Bidder’s profit (bid – price if wins, or 0 Bidder’s profit (bid – price if wins, or 0 otherwise) is maximized when bid is the same otherwise) is maximized when bid is the same as utility for any fixed values for the bids of as utility for any fixed values for the bids of other participantsother participants
Example: VickreyExample: Vickrey Counterexample: First price sealed bidCounterexample: First price sealed bid Why is this important?Why is this important?
Revenue is maximized in truthful auctionsRevenue is maximized in truthful auctions
Truthful Auction Truthful Auction ExampleExample
Imagine participating in an auction Imagine participating in an auction for a jar of 100 pennies that you (and for a jar of 100 pennies that you (and only you) have countedonly you) have counted
In a first price sealed bid auction, In a first price sealed bid auction, you cannot hope to profit by bidding you cannot hope to profit by bidding 100100
In a Vickrey auction, by bidding 100 In a Vickrey auction, by bidding 100 you will at worst break even, but you will at worst break even, but most likely pay lessmost likely pay less
TerminologyTerminology
Competitive auctionsCompetitive auctions Produce revenue within a constant Produce revenue within a constant
factor of optimal fixed pricingfactor of optimal fixed pricing Must vary the number of items sold based Must vary the number of items sold based
on the bids receivedon the bids received Why is this important?Why is this important?
Matching optimal fixed pricing is the best Matching optimal fixed pricing is the best possible resultpossible result
Being within a constant factor is a Being within a constant factor is a reasonable approximationreasonable approximation
Evaluated Auction Evaluated Auction DesignsDesigns
All auctions in this paper are single All auctions in this paper are single round, sealed bidround, sealed bid
Auction mechanisms studied:Auction mechanisms studied: Deterministic Deterministic
Deterministic Optimal ThresholdDeterministic Optimal Threshold RandomizedRandomized
Single PriceSingle Price Dual PriceDual Price Weighted PairingWeighted Pairing
Bid IndependenceBid Independence
Agent’s bid determines whether or Agent’s bid determines whether or not he wins the auction, but not the not he wins the auction, but not the priceprice
Typically multi-price, but not alwaysTypically multi-price, but not always Example: VickreyExample: Vickrey Why is this important?Why is this important?
Bid independence allows for one to bid Bid independence allows for one to bid her utility and still hope for a profither utility and still hope for a profit
Deterministic auctions must be bid Deterministic auctions must be bid independent in order to be truthfulindependent in order to be truthful
Truthful Deterministic Truthful Deterministic AuctionsAuctions
Consider the Consider the deterministic optimal deterministic optimal threshold auctionthreshold auction To determine if bid bTo determine if bid bii wins wins
Remove bRemove bii from the set of bids (ensure bid from the set of bids (ensure bid independence/truthfulness)independence/truthfulness)
Determine the threshold price at which maximal Determine the threshold price at which maximal revenue is attained in the remaining set of bidsrevenue is attained in the remaining set of bids
If bIf bii >= this threshold, accept b >= this threshold, accept bii at the threshold at the threshold priceprice
Note that this removal of bi is the only thing Note that this removal of bi is the only thing that differentiates this auction from optimal that differentiates this auction from optimal fixed pricingfixed pricing
Deterministic Optimal Deterministic Optimal Threshold Auction ExampleThreshold Auction Example
3 3 3 2 2 15
Step 1: Remove the bid to be evaluated:3
Step 2: Compute the optimal threshold on the remaining bids:
3 3 2 2 15
Sell1 at 5: 53 at 3: 95 at 2: 106 at 1: 6Optimal threshold is 2
Step 3: Compare the removed bid to the optimal threshold3 > 2
Step 4: Accept bid 3 at price 2
Truthful Deterministic Truthful Deterministic AuctionsAuctions
Theoretical ResultsTheoretical Results Truthful Deterministic Bid-Truthful Deterministic Bid-
Independent Auctions are not Independent Auctions are not Competitive in the worst caseCompetitive in the worst case
Removing bRemoving bii causes bigger problems causes bigger problems than one would expectthan one would expect
Consider an input set where the high Consider an input set where the high bid bid hh occurs occurs rr times, and there are times, and there are ((h – 1) (r – 1) h – 1) (r – 1) other bids at 1other bids at 1
Proof SketchProof Sketch
Example: Example: hh = 5, = 5, rr = 3 = 3
5 5 5 1 1 1 1 1 1 11
Sell… • 11 at price 1 (11 revenue)• 3 at price 5 (15 revenue)
Proof Sketch, ContinuedProof Sketch, Continued
Deterministic Optimal Threshold Deterministic Optimal Threshold Auction on this input:Auction on this input:
5 5 5 1 1 1 1 1 1 11
5 5 5 1 1 1 1 1 1 11
To determine if b1 wins, remove it and compute To determine if b1 wins, remove it and compute the threshold on the rest of the inputthe threshold on the rest of the input
Sell 2 units at 5, or 10 units at 1 Threshold falls to 1, so end up selling Threshold falls to 1, so end up selling
to the high bids at the low priceto the high bids at the low price
More ResultsMore Results This result generalizes to all This result generalizes to all
Deterministic Auctions due to the Deterministic Auctions due to the theorem that all Truthful Deterministic theorem that all Truthful Deterministic Auctions are Bid IndependentAuctions are Bid Independent
Proof intuition:Proof intuition: Can’t profit by bidding utility if you’ll pay it Can’t profit by bidding utility if you’ll pay it
upon winningupon winning Paper goes on to present empirical Paper goes on to present empirical
evidence that on realistic data, the worst evidence that on realistic data, the worst case for these auctions doesn’t come up case for these auctions doesn’t come up oftenoften
Random Sampling AuctionsRandom Sampling AuctionsMotivationMotivation
Auction mechanisms need not only Auction mechanisms need not only be resistant to bad inputs, but also be resistant to bad inputs, but also to attackto attack
By using some nondeterminism in By using some nondeterminism in deciding who wins and at what deciding who wins and at what price, we can avoid dominance by price, we can avoid dominance by worst case inputsworst case inputs
Random Sampling Random Sampling AuctionsAuctions
Choose a random sample from the set of bidsChoose a random sample from the set of bids Run the optimal threshold function on the Run the optimal threshold function on the
sample and use the result on the bids not in the sample and use the result on the bids not in the samplesample
Single priceSingle price NondeterministicNondeterministic Dual price variant:Dual price variant:
Choose roughly half of the bids for the sampleChoose roughly half of the bids for the sample Calculate thresholds on both setsCalculate thresholds on both sets Use the threshold from one set on the other, and vice Use the threshold from one set on the other, and vice
versaversa Avoids having to throw out bids from the sampleAvoids having to throw out bids from the sample
Random Sampling Random Sampling ExampleExample3 3 3 2 2 1
Step 1: Choose subset at random: 3 2
5
2
Step 2: Compute optimal threshold: 3 2 2
Sell 1 at 3: 3Sell 3 at 2: 6Optimal threshold is 2
Step 3: Apply optimal threshold to those not in the sample:
3 3 15
Step 4:
Accept 3 35 at price 2
Random Sampling AuctionsRandom Sampling AuctionsTheoretical ResultsTheoretical Results
Random sampling auctions are competitive Random sampling auctions are competitive Revenue generated is within a constant factor of Revenue generated is within a constant factor of
optimal fixed pricing with arbitrarily high (but not optimal fixed pricing with arbitrarily high (but not 1.0) probability1.0) probability
The higher the probability, the lower the constantThe higher the probability, the lower the constant General flavor of the proof:General flavor of the proof:
The chosen subset is a good representation of the The chosen subset is a good representation of the whole most of the timewhole most of the time
The revenue lost from losing the sampled bids is The revenue lost from losing the sampled bids is a constant factor of the wholea constant factor of the whole
The dual price version performs even betterThe dual price version performs even better
Weighted Pairing Weighted Pairing AuctionsAuctions
To determine if a particular bidder i wins To determine if a particular bidder i wins with bid bi:with bid bi: Choose another bid b with probability Choose another bid b with probability
proportional to its value –higher bids get picked proportional to its value –higher bids get picked more oftenmore often
Compare b with bi. If bCompare b with bi. If bii >= b, bidder i wins and >= b, bidder i wins and pays bpays b
Multi-priceMulti-price NondeterministicNondeterministic High bidders likely to win and pay high High bidders likely to win and pay high
prices, but some low bidders sneak in as wellprices, but some low bidders sneak in as well
Weighted Pairing Weighted Pairing ExampleExample3 3 3 2 2 15
Step 1: Choose a bid 3
Step 2: Choose another bid with probability proportional to its value
2Step 3: Compare 3 >
Step 4: Bid 3wins and pays price 2
2
Weighted Pairing AuctionsWeighted Pairing AuctionsTheoretical ResultsTheoretical Results
Weighted Pairing auctions are not Weighted Pairing auctions are not quite competitivequite competitive
Within a logarithmic factor of fixed Within a logarithmic factor of fixed pricing, so not bad eitherpricing, so not bad either
Perform well on inputs that random Perform well on inputs that random sampling does notsampling does not