Intermediate Microeconomics and Its Application 12th Edition by Walter Nicholson,Christopher Snyder

Exercise 22

Tess and Meg are the only two bidders in an auction for a van Gogh painting. Each can be one of two types with equal probability: a low-value consumer with valuation $1 million or a high-value consumer with valuation $2 million. Each knows her own type but only knows the probabilities of the other's type.
a. Suppose they compete in a sealed-bid, second price auction. What are the equilibrium bidding strategies? Compute the seller's expected revenue.
b. Repeat part a supposing there are three identical bidders. What if there are N bidders?
c. Explain how your answer from parts a and b can be used to compute the seller's expected revenue from a first-price, sealed-bid auction.