Auction Seminar : Revenue Equivalence

Auction Seminar : Revenue EquivalencePresentation by Liran ZusmanSupervised by Amos Fiat

: 1Our Goals : BNE BNE

:

CurriculumQuick ReviewCharacterization of Bayes-Nash EquilibriumRevenue EquivalenceExamplesDesigning auctions to maximize profit

, 4DefinitionsLemma7Characterization of Bayes-Nash Equilibrium : , , . Sanity check. 1,3, . , .

8Proof Sketch ! . .9Notes10Revenue Equivalence

11One Last Corollary

Proof13

First-Price Auction

15Why is it BNE?16Dominated bid

17Example18What Does It Mean?

All-Pay Auction: !

: . . , !

: !

Claim

: Vickrey, F. , .21ProofWar-of-Attrition Auction :

Vickrey. ...

!: ,

Motivation , :

. . , . . , .

: ...Claim

Proof26

Something to Think About :

2 , .

: , ., .

, ...Designing Auctions to Maximize ProfitIntroduction , . , !

, ?? Revenue Equivalence: , ., , .30Possible Solution Second-Price Auction : Truthful, , . ?

!

2nd price - 1990, 100,000$ - 6$ !!

Vickrey ?: 31Reserve Price:Vickrey Auction with a reserve price r Sealed-bid Second-Price Auction, r, r .

: Vickrey Truthful

: , Vickrey , -r. .

Proof Vickrey r. Truthful:

n . n+1, r. Vickrey , : n -r, .

" ", (=) Truthful .ExampleAnalysis

35Analysis cnt.Homework

37Thanks for Listening