Consider an item put in an auction with the following rule: Each bidder submits one bid in a sealed envelope to the auction. The envelopes are open, and the highest bid gets the good. The price paid by that bidder is equal to the second highest bid that was submitted. Assume each bidder i has a valuation for the good (i.e. a maximum willingness to pay) equal to 0;. If a bidder does not get the item, he gets a utility of O. If a bidder wins, his utility is equal to 0; minus the price paid (the second highest bid). (a) (2 points) What are the possible strategies for each bidder? (b) (2 points) Consider bidder i. Assume he decides to submit a bid bi = 0;. What are the possible outcomes of such a strategy? (an outcome includes whether the bidder gets the item, how much he pays and what his utility is) (c)(3 points) Compare the utility bidder i gets if he bids b; < 0; instead of bi 0;. Is there a situation where bidder i should bet bi 0; instead of b; <0;? Is there a situation where he should bet b; < 0; instead of bi 0; ? (think about different situations regarding how big the second highest bid is) = (d) (3 points) Is there a situation where bidder i should bet bi = 0; instead of bi >0;? Is there a situation where he should bet b; > 0, instead of b; = 0; ? (think about different situations regarding how big the second highest bid is) (e) (3 points) Items (a), (b) and (c) show three possible strategies: b = 0; b; < 0; bi > Oi Using your previous answers, conclude which strategy dominates the others and deduce the Nash equilibrium of such an auction.