Q4 Equilibrium Analysis of the Uniform Price auction Consider a uniform price (highest-rejected 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 unit at per unit price p generates 10 — p. Let's denote (xi, Yi) (where xi ≥ yi) a bidding strategy of bidder i where x is the declared marginal value for the first 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 xi, Yi must be integers. (a) Write down the corresponding demand curve when bidder 1 bids (x₁ = 8, y₁ = 4). (b) It is well-known that bidders have a weakly dominant strategy in the uniform-price auctions with the highest-rejected bid pricing rule. What does it imply for a strategy (x1,y1) for bidder 1 and (x2, y2) for bidder 2? For parts (c) and (d), assume that both bidders follow their weakly dominant strategies that you have identified 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? What is the lowest revenue that the seller can get in an equilibrium? 2