(Riley and Samuelson 1981): Consider an auction with two buyers with valuations drawn independently from the uniform [0, 1] distribution. The seller sets a reserve price equal to 1 and she employs the following auction rules:
(a) There is a single round of bidding. Buyer 1 is given the opportunity to make a bid a price b1 ≥ 1 .
(b) If buyer 1 bids b1 ≥ 1 , buyer 2 can match b1 and win the object. If buyer 1 makes no bid, buyer 2 can obtain the good at price 1 if he
so chooses.
(i) Does this auction resemble any selling mechanism that you know of?
(ii) Can you compute the buyers' equilibrium bidding strategies and the seller's expected revenue?
(iii) Is the object in equilibrium always allocated to the individual with the highest valuation?
(iv) Compare the expected revenue generated by this auction with the expected revenue generated by a second-price auction with reserve price equal to 1.