Consider a first-price sealed-bid auction of an object with two bidders. Each bidder i's valuation of the object is v₁ ≥ 2, which is known to both bidders, i = 1,2. The auction rules are that each player submits a bid in a sealed envelope. The envelopes are then opened, and the bidder who has submitted the highest bid gets the object and pays the auctioneer the amount of his bid. If the bidders submit the same bid, each gets the object with probability 1/2. Bids must be in dollar multiples (assume that the valuations are also). i. Specify bidders payoffs as functions of their valuations and bids. ii. Are any strategies strictly dominated? Are any strategies weakly dominated? Explain. iii. Derive the best response correspondences for each player. iv. Is there a Nash equilibrium (in pure strategies)? If yes, what is it? Is it unique? Carefully explain all your answers.