{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

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

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 ) = 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 utility is therefore Pr braceleftbig β 1 ( b i ) ω j

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.

{[ snackBarMessage ]}