Strategic Bidding in Strategic Bidding in AuctionsAuctions

Phil HailePhil Haile

Yale UniversityYale University

Prevalent Auction TypesPrevalent Auction Types

Ascending Auction (a.k.a. English Ascending Auction (a.k.a. English auction)auction) antiques, art, cattle, used cars, eBay, timberantiques, art, cattle, used cars, eBay, timber

First-Price Sealed-bid AuctionFirst-Price Sealed-bid Auction offshore drilling rightsoffshore drilling rights public and private procurement (bidders are public and private procurement (bidders are

sellers, sellers, lowlow bidder wins) bidder wins) Descending Auction (a.k.a. Dutch Descending Auction (a.k.a. Dutch

Auction)Auction) flowers, fish, plantsflowers, fish, plants

Why hold an auction?Why hold an auction? Seller uncertain what the good is worth Seller uncertain what the good is worth

unique items (antique, Monet painting)unique items (antique, Monet painting) items difficult to evaluate (timber/oil rights)items difficult to evaluate (timber/oil rights) demand shocks (financial markets)demand shocks (financial markets)

Important to sell quickly (fresh fish, Important to sell quickly (fresh fish, flowers)flowers)

Seller wants to allocate efficiently Seller wants to allocate efficiently (or at least, to bidder willing to pay the (or at least, to bidder willing to pay the most e.g., FCC spectrum auctions)most e.g., FCC spectrum auctions)

Auction 1Auction 1

For sale: contents of envelopeFor sale: contents of envelope golf tees worth 1 cent eachgolf tees worth 1 cent each if X tees, $X/100 in envelopeif X tees, $X/100 in envelope

Ascending AuctionAscending Auction Winner of the auction (high bidder)Winner of the auction (high bidder)

gets the envelopegets the envelope pays me his final bid bpays me his final bid b (net profit = $X/100 – $b)(net profit = $X/100 – $b)

COUNTCOUNT

596 tees596 tees

Auction 2Auction 2

For sale: empty envelopeFor sale: empty envelope student ID card: last 3 SID student ID card: last 3 SID

numbers=your valuation of the numbers=your valuation of the envelope in centsenvelope in cents e.g., mine=$5.08e.g., mine=$5.08

I pay the winner his/her valuationI pay the winner his/her valuation Winner pays me his/her final bid bWinner pays me his/her final bid b

net profit = winner’s valuation – bnet profit = winner’s valuation – b

What was different about these two What was different about these two auctions?auctions?

A Key DistinctionA Key Distinction

YES: “YES: “common values auctioncommon values auction’’’’ examplesexamples

our first auctionour first auction oil drilling rights (?) oil drilling rights (?)

Do other bidders have information that would be useful to you in determining your own valuation for the good?

A Key Distinction (2)A Key Distinction (2)

NO: “NO: “private values auctionprivate values auction’’’’ examples:examples:

our second auctionour second auction many eBay auctions (?)many eBay auctions (?)

Do other bidders have information that would be useful to you in determining your own valuation for the good?

Common Values Common Values and the Winner’s Curseand the Winner’s Curse

Example: Auction for oil drilling rightsExample: Auction for oil drilling rights given quantity of oil in the groundgiven quantity of oil in the ground prices, extraction costs same for all biddersprices, extraction costs same for all bidders bidders have different estimates (“signals”)bidders have different estimates (“signals”) signals are noisy but correct on averagesignals are noisy but correct on average

Suppose bidder with highest signal bids Suppose bidder with highest signal bids mostmost highest signal=most optimistic signalhighest signal=most optimistic signal most optimistic = most optimistic = overlyoverly optimistic optimistic

(usually)(usually)

The Winner’s CurseThe Winner’s Curse

A bidder who ignores the fact that he wins only when his signal is unusually optimistic may regret his bid when he wins -- e.g., pay more than he needed to or more than the true expected value of the good to him.

$@#%! I paid too much!

Avoiding the Winner’s Avoiding the Winner’s CurseCurse

““Why are the others letting me win Why are the others letting me win at this price?”at this price?”

““Do I really want to pay this much, Do I really want to pay this much, even if no one else is?”even if no one else is?”

““What do I think the good is worth to What do I think the good is worth to me, assuming others’ information me, assuming others’ information tells them to bid less than I bid?”tells them to bid less than I bid?”

Rational bidders avoid the winner’s Rational bidders avoid the winner’s curse by thinking strategicallycurse by thinking strategically

Adverse SelectionAdverse Selection

Used car market: “Why is the owner Used car market: “Why is the owner willing to sell the car at this price’’? willing to sell the car at this price’’?

Insurance market: “Why does this Insurance market: “Why does this customer want to buy so much customer want to buy so much insurance?”insurance?”

Dating: “Why is s/he willing to go out Dating: “Why is s/he willing to go out with me?”with me?”

Winner’s curse just one example . . . others:

in theory, AS can lead to inefficienciencies, even to missing markets (Akerlof 2001 Nobel Prize). In an auction, it can make bidders hesitant to bid agressively.

Strategic Thinking by Strategic Thinking by Bidders: TheoryBidders: Theory

Account for the winner’s curse (if a Account for the winner’s curse (if a common values auction)common values auction)

How much to bid?How much to bid? Ascending auction with private values: Ascending auction with private values:

optimal to bid up to valuation (dominant optimal to bid up to valuation (dominant strategy)strategy)

First-price sealed bid auction: shade bid First-price sealed bid auction: shade bid below valuation…but how much? below valuation…but how much? MB: pay less when winMB: pay less when win MC: may not winMC: may not win

must balance

Bayesian Nash equilibrium: each bidder shades optimally, knowing that all others are too

Bid $1 less, saves a dollar if winsdepends on

Pr(next highest bid is just below mine)

Strategic Bidding:Strategic Bidding:Empirical EvidenceEmpirical Evidence

Oil drilling rights auctions (FPSB)Oil drilling rights auctions (FPSB) Data: bids, realized value of oilData: bids, realized value of oil bids are below expected valuesbids are below expected values bidders don’t bid aggressively against bidders don’t bid aggressively against

better informed competitorsbetter informed competitors measure marginal cost of shading: measure marginal cost of shading:

bidders seem to optimally trade off MC bidders seem to optimally trade off MC and MBand MB

Strategic Bidding by Strategic Bidding by Bidders:Bidders:

Empirical Evidence (2)Empirical Evidence (2)USFS timber auctions (FPSB)USFS timber auctions (FPSB) Data: bids, auction characteristicsData: bids, auction characteristics in theory, winner’s curse more severe in theory, winner’s curse more severe

when face more competitors in common when face more competitors in common values auctionvalues auction

Does this hold in practice?Does this hold in practice?Most optimistic out of 2 isn’t “extremely” overly optimistic

Most optimistic out of 10 is!

USFS timber auctions (2)USFS timber auctions (2) How to measure empirically?How to measure empirically? MB vs. MC of increasing bid:MB vs. MC of increasing bid:

[v[vii*(n) – b] d/db Pr(b wins|n) = Pr(b wins|n) *(n) – b] d/db Pr(b wins|n) = Pr(b wins|n) ×1×1

MB: raise probability of winning

MC: pay more when win

≡expected value of winning against n-1 competitors in eqm

USFS timber auctions (2)USFS timber auctions (2) How to measure empirically?How to measure empirically? MB vs. MC of increasing bid:MB vs. MC of increasing bid:

[v[vii*(n) – b] d/db Pr(b wins|n) = Pr(b wins|n) *(n) – b] d/db Pr(b wins|n) = Pr(b wins|n) ×1×1

can estimate using bid data

can estimate using bid data

observable

So we can estimate this!

Rational bidding requires vRational bidding requires vii*(n) to *(n) to decrease with n decrease with n

So test this. (results: yes when bidders So test this. (results: yes when bidders face common uncertainty and have face common uncertainty and have opportunity to acquire signals)opportunity to acquire signals)

Auctions as Testing Auctions as Testing GroundGround

data + equilibrium relations from theory data + equilibrium relations from theory can reveal unobservable things can reveal unobservable things determining how markets workdetermining how markets work

trust in results requires trust in trust in results requires trust in equilibrium relations from theoryequilibrium relations from theory

with auctions, unusually close match with auctions, unusually close match between theoretical model and actual between theoretical model and actual marketmarket

∴ ∴ ideal for testing, learning about things ideal for testing, learning about things that are hard to assess in other markets that are hard to assess in other markets (e.g., subprime crisis, front-running)(e.g., subprime crisis, front-running)

Strategic Thinking for Strategic Thinking for SellersSellers

What kind of auction to hold if want to . . .What kind of auction to hold if want to . . . maximize revenue (minimize cost)maximize revenue (minimize cost) ensure efficient allocationensure efficient allocation

What is optimal reserve price?What is optimal reserve price? Sell units all at once, one by one, in Sell units all at once, one by one, in

bundles. . . ?bundles. . . ? How to prevent collusion?How to prevent collusion?

Answers require anticipating strategic bidding, and often depend on details of demand and information structure

Example: Treasury Bill Example: Treasury Bill AuctionsAuctions

Multi-unit auctions: bidders offer a Multi-unit auctions: bidders offer a “demand curve” of price-quantity pairs“demand curve” of price-quantity pairs

p

qQ

S

Sum of all bidders’ offers

p*

D

Example: Treasury Bill Example: Treasury Bill AuctionsAuctions

p

q

bidder i’s offersp*

Uniform price auction: price p* for all Uniform price auction: price p* for all unitsunits

revenue

Example: Treasury Bill Example: Treasury Bill AuctionsAuctions

p

q

bidder i’s offersp*

Discriminatory auction: “pay your bid” on Discriminatory auction: “pay your bid” on each uniteach unit

revenue Note: offers will not the same as in uniform price auction because bidders are strategic!

qi

revenue

Which auction maximizes Which auction maximizes revenue?revenue?

Theory: ambiguous, depends on Theory: ambiguous, depends on bidder valuationsbidder valuations

Experiments: clouded by simultaneous Experiments: clouded by simultaneous changes in macroeconomy, changes in macroeconomy, regulations, financial marketsregulations, financial markets

empirical aproach: estimate the empirical aproach: estimate the primitives determining demand, then primitives determining demand, then simulate what would happen under simulate what would happen under each type of selling mechanismeach type of selling mechanism

results so far: it matters very little!results so far: it matters very little!

Revenue EquivalenceRevenue Equivalence

For some cases, theory tells us many For some cases, theory tells us many auctions (including first-price, auctions (including first-price, Dutch, and ascending) should give Dutch, and ascending) should give the same expected revenuethe same expected revenue

Revenue EquivalenceRevenue Equivalence

For For some casessome cases, theory tells us many , theory tells us many auctions (including first-price, auctions (including first-price, Dutch, and ascending) should give Dutch, and ascending) should give the same expected revenuethe same expected revenue symmetric independent private valuessymmetric independent private values

Vickrey Nobel Prize in 1996Vickrey Nobel Prize in 1996

Revenue Equivalence: Revenue Equivalence: IntuitionIntuition

Ascending auction: bid up to valuationAscending auction: bid up to valuation so price = 2so price = 2ndnd highest valuation highest valuation

First-price auctionFirst-price auction shade bid below valuationshade bid below valuation optimal bid=best guess of next highest optimal bid=best guess of next highest

valuation, valuation, assuming your own bid will winassuming your own bid will win assumptionassumption correct for winner correct for winner so price=unbiased guess of 2so price=unbiased guess of 2ndnd highest highest

valuationvaluation

Revenue Equivalence: Revenue Equivalence: IntuitionIntuition

Ascending auction: bid up to valuationAscending auction: bid up to valuation so so price = 2price = 2ndnd highest valuation highest valuation

First-price auctionFirst-price auction shade bid below valuationshade bid below valuation optimal bid=best guess of next highest optimal bid=best guess of next highest

valuation, assuming your own bid will winvaluation, assuming your own bid will win assumption correct for winnerassumption correct for winner so so price=unbiased guess of 2price=unbiased guess of 2ndnd highest highest

valuationvaluation

Want to learn more?Want to learn more?

Theory Theory V. Krishna, V. Krishna, Auction TheoryAuction Theory, 2002, 2002 P. McAfee and J. McMillan (1989), P. McAfee and J. McMillan (1989),

“Auctions and Bidding: A Primer,” J. “Auctions and Bidding: A Primer,” J. Economic PerspectivesEconomic Perspectives

Empirical workEmpirical work K. Hendricks & R. Porter (2007), “Lectures K. Hendricks & R. Porter (2007), “Lectures

on Auctions: An Empirical Perspective” (on on Auctions: An Empirical Perspective” (on the web)the web)

S. Athey & P. Haile (2007), “Empirical S. Athey & P. Haile (2007), “Empirical Models of Auctions” (on my Yale web page)Models of Auctions” (on my Yale web page)