Question: Consider the private value auction model, with n bidders. Each bidder's value is drawn independently from U[0,100]. (a) Suppose the seller runs a second-price auction.

Consider the private value auction model, with n bidders. Each bidder's value is drawn independently from U[0,100].

(a) Suppose the seller runs a second-price auction. What is the expected selling price, and the expected valuation of the winning bidder?

(b) From an ex-ante perspective, that is, before the bidders have learned their private values, what is the expected payo of any given bidder?

(c) Suppose that there are a large number of potential entrants, but only some will decide to participate the auction. That is, each potential bidder decides invest an amount k = 5 to learns her value. Only after such investment, she observes how many other bidders entered (i.e., invested 5 and learned their values). A standard second-price auction follows. How many bidders will enter the auction? (Note: in equilibrium, each entrant will expect at least zero prot from entering, and each non-entrant expects a negative prot it were to enter.)

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