Q4 Equilibrium Analysis of the Uniform Price auction Cansider a uniform price [highestrejected bid sets the price} auction with two bidders. The auctioneer offers two identical Imits 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 Imits at per unit price 31! generates payoff of 20 2p and winning one unit at per lmit price p generates 10 p. Let's denote (rhyg) (where 3::- 2 ii) a bidding strategy of bidder 2' where r;- is the declared marginal value for the rst item, and 1,5; is the declared marginal value for the second item. Suppose that bidders are restricted to using integers for their marginal values, so both Ii, 1;,- 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 {331, m} for bidder 1 and {332, 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)I Suppose that bidder 1 bids [10, 5}. How would bidder 2 bid in response? (d) Now describe all pure strategy,r Nash equilibria of this auction game? What is the lowest revenue that the seller can get in an equilibriunl