You are a bidder in an independent private values auction, and you value the object at $4,500. Each bidder perceives that valuations are uniformly distributed between $500 and $9,000. Determine your optimal bidding strategy in a first-price, sealed-bid auction when the total number of bidders (including you) is:   a. 2 bidders. Bid: $  b. 10 bidders. Bid: $  c. 100 bidders. Bid: $

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How to solve this question? Consider an antique auction where bidders have independent private values. There are two bidders, each of whom perceives that valuations are uniformly distributed between $100 and $1,000. One of the bidders is Sue, who knows her own valuation is $200. What is Sue's optimal bidding strategy in a Dutch auction?

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Consider a sealed-bid auction in which the seller draws one of the N bids at random. The buyer whose bid was drawn wins the auction and pays the amount bid. Assume that buyer valuations follow a uniform(0,1) distribution. 1. What is the symmetric equilibrium bidding strategy b(v)?2. What is the seller’s expected revenue?3. Why doesn’t this auction pay the seller the same revenue as the four standard auctions? That is, why doesn’t the revenue equivalence theorem apply here?

Discrete All-Pay Auction: In Section 6.1.4 we introduced a version of an all- pay auction that worked as follows: Each bidder submits a bid. The highest bidder gets the good, but all bidders pay their bids. Consider an auction in which player 1 values the item at 3 while player 2 values the item at 5. Each player can bid either 0, 1, or 2. If player i bids more than player j then i wins the good and both pay. If both players bid the same amount then a coin is tossed to determine who gets the good, but again both pay. a. Write down the game in matrix form. Which strategies survive IESDS? b. Find the Nash equilibria for this game.

You are one of five risk-neutral bidders participating in an independent private values auction. Each bidder perceives that bidders' valuations for the item are evenly distributed between $20,000 and $50,000. For each of the following auction t determine your optimal bidding strategy if you value the item at $35,000. a. First-price, sealed-bid auction. O Bid $20,00. O Bid $50,00. O Bid $35,00. O Bid $32,000 b. Dutch auction O Let the auctioneer continue to lower the price until it reaches $20,000, and then yell "Minel". O Let the auctioneer continue to lower the price until it reaches $35.000, and then yell "Mine!" O Let the auctioneer continue to lower the price until it reaches $32,000, and then yell "Mine!" O Let the auctioneer continue to lower the price until it reaches $50,000, and then yell "Mine!". C. ond-price, sealed-bid auction O Bid $50,00. O Bid $35.000 O Bid $32,00. b. Dutch auction. O Let the auctioneer continue to lower the price until it reaches $20,000, and then yell…

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Economics Consider a first-price sealed-bid auction of a single object with two bidders j = 1, 2. Bidder 1's valuation is v1 = 2, and bidder 2' s valuation is v2 = 5. Both v1 and v2 are known to both bidders. Bids must be in whole dollar amounts (e.g. $1). In the event of a tie, the object is awarded by a flip of a fair coin. (a) Write down this auction as a 2 × 2 matrix game. Hint: note that each bidder can choose a bid from {0, 1, 2, 3, 4, 5, ..}. Your matrix will be incomplete since you cannot write a matrix with infinite rows and columns (b) Eliminate the strictly dominated strategies. Write down the resulting matrix game. (c) An auction is efficient if the good is allocated to the bidder with the highest valuation of the good. What are the Nash equilibria of this game? Åre the Nash equilibria efficient? %3D

Suppose there are three bidders with values for the object that are independent, private and uniformly distributed over [0, 1]. a) Derive the seller's expected revenue in a second-price auction. Fully explain your answer. b) Derive the seller's expected revenue in a first-price auction. Fully explain your answer. c) Explain why the answers to parts (a) and (b) are the same. d) Show that the answers to parts (a) and (b) remain the same when there are N bidders. Fully explain your answer.