Consider a standard first-price auction for a single object. There are three bidders (N = 3) with valuations independently drawn from the uniform distribution on [200, 300). Calculate the auctioneer's expected revenue in the efficient equilibrium of this auction. Type your answer.
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- You are a bidder in an independent private auction, and you value the object at $2000. Each bidder assumes that the valuations are uniformly distributed between $1000 and $5000. Determine your optimal bidding strategy in a first-price sealed bid auction when the total number of bidders are: 2, 10, and 100.(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.In a first-price auction, bidding one’s valuation weakly dominates bidding any higher real number
- 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?You are one of five risk-neutral bidders participating in an independent private values auction. Each bidder perceives that all other bidders’ valuations for the item are evenly distributed between $10,000 and $30,000. For each of the following auction types, determine your optimal bidding strategy if you value the item at $22,000. a. First-price, sealed-bid auction. b. Dutch auction. c. Second-price, sealed-bid auction. d. English auction.There are three bidders participating in a first-price auction for a painting. Each bidder has a private, independent value vi for such a painting that is drawn uniformly from [0,1] Assume that each bidder i has a linear bidding function bi=avi, where a>0. What is the bidding strategy of bidder i , namely bi in the Bayesian equilibrium?
- 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: $Suppose there are N bidders competing for a single object in an all-pay auction. Each bidder has an i.i.d value vi for the object drawn from some continuous distribution F with support [0, M ]. (a) Show that there is a symmetric equilibrium in increasing strategies. (b) What is the expected revenue generated by this auction in the equilibrium from (a)? Elaborate the explanation on both the answers.Consider the charity auction. In many charity auctions, altruistic celebrities auction objects with special value for their fans to raise funds for charity. Madonna, for example, held an auction to sell clothing worn during her career and raised about 3.2 million dollars. In the charity auction the winner of the lot is the highest bidder. The difference with the standard auction is that all bidders are required to pay an amount equal to what they bid. Suppose there are two bidders and assume bidders have valuations randomly drawn from the interval [2, 4] according to the uniform distribution. 1. Derive the equilibrium bidding function. Hint: After getting the differential equation given by the FOC, propose a non-linear bidding function b(v) = α + βv2 as solution. Your task is to find α and β. 2. Derive the revenue of the seller in the charity auction. 3. Would the seller obtain higher profits if she organized a first-price sealed bid auction instead? A. Yes, higher revenue B. No, lower…
- Consider a Common Value auction with two bidders who both receive a signal X that is uniformly distributed between 0 and 1. The (common) value V of the good the players are bidding for is the average of the two signals, i.e. V = (X1+X2)/2. Compute the symmetric Nash equilibrium bidding strategy for the second-price sealed-bid auction assuming that players are risk-neutral and have standard selfish preferences. Furthermore, you may assume that the other bidder is following a linear bidding strategy. Make sure to explain your notation and the steps you take to derive the result.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?Consider a Common Value auction with two bidders who both receive a signal X that is uniformly distributed between 0 and 1. The (common) value V of the good the players are bidding for is the average of the two signals, i.e. V = (X1+X2)/2. the symmetric Nash equilibrium bidding strategy for the second-price sealed-bid auction assuming that players are risk-neutral and have standard selfish preferences. Furthermore, you may assume that the other bidder is following a linear bidding strategy. Make sure to explain your notation and the steps you take to derive the result.