Q4 Equilibrium Analysis of the Uniform Price auction Consider a uniform prioe [highestrejected bid sets the price] auction with two bidders. The auctioneer offers two identical units of the same product for sale. Each bidder values each unit at $10 [i.e., it is a complete information auction game), so winning two units at per unit price p generates payoff of 20 2p and winning one 1mit at per unit price p generates 10 19. Let's denote (33,315) (where 3:, 2 1,} a bidding strategy of bidder i where :12,- is the declared marginal value for the rst item, and y,- is the declared marginal value for the second item. Suppose that bidders are restricted to using integers for their marginal values, so both why, must be integers. (a) Write down the corresponding demand curve when bidder 1 bids (3:1 = 8, y1 = 4]. (b) It is wellknown that bidders have a weakly dominant strategy in the uniformprice auctions with the highestrejected bid pricing rule. What does it imply for a strategy (1'1, yl} for bidder 1 and [3:2, 9'2] for bidder 2? For parts [c] and (d), assume that both bidders follow their weakly dominant strategies that you have identied in part (b). (c) Suppose that bidder 1 bids {10, 5). How would bidder 2 bid in response? (d) Now describe all pure strategy Nash equilibria of this auction game? 1What is the lowest revenue that the seller can get in an equilibrimn