Matching Auction Consider an auction with two buyers with valuations drawn independently from the uniform distribution on [0, 1]. The seller sets a reserve price equal to 1 2 and she employs the following auction rules:

(i) First, buyer 1 is given the opportunity to bid b1 1 2 .

(ii) If buyer 1 bids b1 1 2 , then buyer 2 can match b1 and win the object. If buyer 1 makes no bid, buyer 2 can obtain the good at price 1 2 if he so chooses.

Given these stated auction rules, please answer the following questions. Please explain and show your work.

(a) Compute the buyers' equilibrium bidding strategies and the seller's expected revenue. (b) Is the object always allocated to the individual with the highest valuation?

(c) Compare the expected revenue generated by this auction with the expected revenue generated by a second-price auction with reserve price equal to 1/2