18.11 Increasing competition in an auction A painting is auctioned to distributed between 0 and 1. bidders, each with a private value for the painting that is uniformly

a. Compute the equilibrium bidding strategy in a first-price sealed-bid auction. Compute the seller's expected revenue in this auction. Hint: Use the formula for the expected value of the kth-order statistic for uniform distributions in Equation 18.70.

b. Compute the equilibrium bidding strategy in a second-price sealed-bid auction. Compute the seller's expected revenue in this auction using the hint from part (a).

c. Do the two auction formats exhibit revenue equivalence?

d. For each auction format, how do bidders' strategies and the seller's revenue change with an increase in the number of bidders?