Explain why a player in a sealed-bid, second-price auction would never submit a bid that exceeds his or her true value of the object being sold. (Hint: What if all players submitted bids greater than their valuations of the object?)
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Explain why a player in a sealed-bid, second-price auction would never submit a bid that exceeds his or her true value of the object being sold. (Hint: What if all players submitted bids greater than their valuations of the object?)
Sealed Bid:
A sealed bid is a process in which the price of the goods is bid under the sealed packet and the bidder does not have the idea of other bidders’ bid.
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- Question 3: Auction Theory a) What is the difference between a common value auction and a private value auction? b) What is meant by the winner’s curse? c) Is there a winner's curse on a private value auction?See attachments for question context. Question: Some people advocated the following modifiction of the auction rule. A bidder cannot bid for only one object, i.e., if at some point in time he withdraws from the bidding race for one object, he automatically withdraws the race for the other object. Every other aspect of the auction, including how prices increase over time, does not change. What should a bidder do if his valuation for the two objects are 50 and 60, respectively? Explain. Does the auction lead to an efficient allocation? Explain.Consider the following situation: five individuals are participating in an auction for an old bicycle used by a famous cyclist. The table below provides the bidders' valuations of the cycle. The auctioneer starts the bid at an offer price far above the bidders' values and lowers the price in increments until one of the bidders accepts the offer. Bidder Value ($) Roberto 750 Claudia 700 Mario 650 Bradley 600 Michelle 550 What is the optimal strategy of each player in this case? Who will win the auction if each bidder places his or her optimal bid? If Claudia wins the auction, how much surplus will she earn?
- 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.Consider a second-price auction (i.e. the highest bid wins, but the winner only pays the second-highest bid), where one bidder is willing to pay much more for the object than anyone else. These are the individual valuations (each bidder only knows their own) Bidder 1 Bidder 2 Bidder 3 Bidder 4 Bidder 5 Bidder 6 Bidder 7 What is the difference between the amount Bidder 2 bids and the amount Bidder 2 pays in equilibrium? 50 O $1,315 $5,600 $3,045 $2,015,400 $5,600 $5,900 $1,500 $3,110 $1,315 O $2,015,400How 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?
- - First-Price and Second-Price Auctions - Consider an auction of a single indi- visible object with 5 bidders, 1, 2, 3, 4 and 5, whose personal valuations (willingness to pay) for the object are v₁ = 10, V₂ = 8, 03 7, 04 5 and 5 3. The bidders simultaneously submit their bids and the winner is the one with the highest bid. Suppose that, when the highest bidder is not unique, the bidder with the smallest number (highest valuation) wins. (a) Suppose that this is a second-price auction, where the winner pays the highest bid among those from her opponents, determine whether each of the following bidding profiles is a Nash equilibrium. Explain. (i) (b₁,b2, b3, b4, b5) = (10, 8, 7, 5, 3) (ii) (b1,b2, b3, b4, b5) = (8,8, 0, 0, 0) (iii) (b₁,b2, b3, b4, b5) = (10, 0, 0, 0, 10) (b) Now suppose that this is a first-price auction, where the winner pays their own bid, determine whether each of the bidding profiles above is a Nash equilibrium. Explain. = =Why it is unwise to bid less than your valuation of the good in a sealed bid second-price auction. In the first price sealed bid auction, a player gets a positive payoff by doing bid shading. Explain the tradeoff between biding lower than the value of the object and biding very close to value of the object.10 Use the expected value information to illustrate how having more bidders in an oral auction will likely result in a higher winning bid.
- 8. Queen Elizabeth has decided to auction off the crown jewels, and there are two bidders: Sultan Hassanal Bolkiah of Brunei and Sheikh Zayed Bin Sultan Al Nahyan of Abu Dhabi. The auction format is as follows: The Sultan and the Sheikh simultaneously submit a written bid. Exhibiting her well-known quirkiness, the Queen specifies that the Sultan's bid must be an odd number (in hundreds of millions of English pounds) between 1 and 9 (that is, it must be 1, 3, 5, 7, or 9) and that the Sultan's bid must be an even number between 2 and 10. The bidder who submits the highest bid wins the jewels and pays a price equal to his bid. (If you recall from Chapter 3, this is a first-price auction.) The win- ning bidder's payoff equals his valuation of the item less the price he pays, whereas the losing bidder's payoff is 0. Assume that the Sultan has a valuation of 8 (hundred million pounds) and that the Sheikh has a valuation of 7. a. In matrix form, write down the strategic form of this game. b.…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(The All-Pay Auction). The seller has an item for sale. The valuations of the bidders are independently and identically distributed on R+ with a c.d.f. F. Find the symmetric equilibrium of an auction with two bidders in which both bidders pay their own bids but only the highest bidder wins the object. Show that each bidder’s expected payment is the same in this auction and in the first-price auction.