Problem 1: Reserve price in SPA. 'Consider a second price auction auction where bidders have values 1:1, 1:2 drawn independently from a uniform distribution on [I], 1] and submit b1, [12. The auctioneer sets a reserve price R > 0 and imposes the following rules: I if bi, bi R and b:- R the second price auction unfolds as ususal. 1. Show that it is still a dominant strategyr for player to bid their true valuation. 2. What is the auctioneer's expected revenue if players play their dominant stragegies'i| Use that lE[Inin(v1,v2|min(c1,u2) 3- R)] = HER 3. Find the reserve price that maximizes the auctioneer's expected revenue. Does the expected revenue increase of decrease compared to a classic second price auction