week13-class

# week13-class - Auctions ECOS3012 Strategic Behavior School...

This preview shows pages 1–5. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Auctions ECOS3012 - Strategic Behavior School of Economics, FASS University of Sydney Lecture 13, June 1, 2011 ECOS3012 - Strategic Behavior (USYD) Auctions Lecture 13, June 1, 2011 1 / 11 Two basic auctions I First price auction (FPA) Consider a symmetric environment with two bidders, whose types are distributed according to a probability distribution function F on an interval [0 , 1] Assume that both players bid according to a bidding function β : [0 , 1]-→ R . Payoff from submitting bid b to a player of type v is U F ( b , β | v ) = ( v- b ) Prob ( b > β ( w )) = v Prob ( w ∈ [0 , 1] | b > β ( w ))- b Prob ( w ∈ [0 , 1] | b > β ( w )) All-pay auction (APA) Payoff from submitting bid b to a player of type v is U A ( b , β | v ) = v Prob ( w ∈ [0 , 1] | b > β ( w ))- b Calculating the equilibrium of an APA is relatively straightforward using a simple trick. ECOS3012 - Strategic Behavior (USYD) Auctions Lecture 13, June 1, 2011 2 / 11 Equilibrium in APA I Suppose β A is the equilibrium bidding function. Equilibrium requires that type v submit the bid β A ( v ) . Therefore, if type v were to mimic the behavior of type v and instead bid β A ( v ) , her should not be better off. That is we must have for all v , v , U A ( β A ( v ) , β A | v ) ≥ U A ( β A ( v ) , β A | v ) (1) Now, let us search for an equilibrium in which higher types bid higher amounts. That is assume that β A is strictly increasing. In fact, let us also assume that β A is differentiable. Then, β A ( v ) > β A ( w ) ⇔ v > w and hence Prob ( w ∈ [0 , 1] β A ( v ) > β A ( w ) ) = F ( v ) (2) and H ( v , v ) = U A ( β A ( v ) , β A | v ) = vF ( v )- β A ( v ) . (3) ECOS3012 - Strategic Behavior (USYD) Auctions Lecture 13, June 1, 2011 3 / 11 Equilibrium in APA II Because of (1), we must have...
View Full Document

{[ snackBarMessage ]}

### Page1 / 11

week13-class - Auctions ECOS3012 Strategic Behavior School...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online