Any value greater or equal than zero for their bid. Announcing a bid is costly for the bidder: if the bidder announces a bid, she incurs a cost c, where wB > c. Passing is free, but the bidder cannot win the object if she passes. If both bidders pass, no bidder wins the object. Otherwise, the bidder with the highest or the final bid wins the object. The auctioneer's payoff is the price at which the object is sold (the winning bid). Bidders maximize their final profit. If a bidder compares two outcomes with the same profit, she prefers the one where she wins the object. The auctioneer calculates the Subgame Perfect Equilibria of this auction and maximizes the price by which it sells the object in these equilibria. (a) How much does each bidder earn in each of the following cases: if she wins, if she bids but is outbid, or if she passes? (b) Assume that bidder A moves first. Find the Subgame Perfect Equilibrium of the auction and describe the strategies used in this SPE. How much do the auctioneer and each bidder earn in this equilibrium? (c) Which bidder would the auctioneer choose to move first? Why? Remember that the auctioneer maximizes the price she can get in the Subgame Perfect Equilibria of this auction. (6 points) (d) Assume as in part (b) that bidder A moves first. Is there a Nash equilibrium of this game in which the object is won by bidder B? If yes, describe the strategies of the bidders in this equilibrium. If not, explain why. Assume now that the auction has three stages: one bidder moves first, the other bidder moves second, and finally, the first mover moves again. Everything else is the same. (e) Which bidder would the auctioneer choose to move first in this case? Why?