PS4 - Problemsets 4 & 5 1. Consider the first-price...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Problemsets 4 & 5 1. Consider the first-price private-value auction where there are n bidders, each with a value drawn from a uniform distribution on [0 , ω ]. If everyone but player i follows a symmetric bidding strategy β ( ω i ), the expected utility of a bid b i is given by: Pr braceleftbig β − 1 ( b i ) ≥ ω j bracerightbig n − 1 [ ω i − b i ] , the probability i ’s bid is the highest multiplied by the payoff if they win. Assume that β ( ω j ) = aω j . (a) Find the best-response bid b ⋆ for bidder i when their value is ω i . (b) Find the value of a such that β ( ω i ) is a symmetric Bayesian Nash equilibrium. (c) Find the expected payment of bidder i . (d) What is the expected payment of bidder i in an all-pay common-value auction? 2. Consider a second-price common-value auction where the value to each player i is given by V i ( ω ) = αω i + (1 − α ) 1 n − 1 ∑ j negationslash = i ( ω j ). Each individual only knows their only component of the value, ω i , and makes a bid b i , and pays the second-highest bid. Again, assume that the individual signals ω i are distributed with a uniform distribution over [0 , ω ]. The expected]....
View Full Document

This note was uploaded on 03/10/2012 for the course ECON 1200 taught by Professor Staff during the Spring '08 term at Pittsburgh.

Page1 / 2

PS4 - Problemsets 4 & 5 1. Consider the first-price...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online