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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?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.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.
- 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: $Explain the differce between oral auctions and second-price auctionsConsider 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…
- 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?(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.Why do sellers generally prefer a Vickrey auction to a regular sealed bid if sellers don’t receive the highest bid in the Vickrey auction? Sellers only have to sell their item if the bid is the highest-price bid. The second-highest bid in a Vickrey auction is generally higher than the highest bid in a regular sealed-bid auction. The second-highest bid is about the same in both auctions. Sellers prefer the final price is not revealed to all bidders. Sellers would never prefer Vickrey auctions.
- You are a bidder in an independent private values auction, and you value the object at $4,000. Each bidder perceives that valuations are uniformly distributed between $1,500 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. b. 10. c. 100Use the expected value information to illustrate how having more bidders in an oral auction will likely result in a higher winning bid.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?