There are 4 bidders with valuations that are independently and uniformly distributed between 0 and 1. In equilibrium, what is the probability that the highest bid is less than 0.2 in a first-price auction? Round your answer to two decimal places.
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- A cool kid is willing to rename himself for a profit. He decides to auctionoff the naming right. Two bidders show interest. Their valuations for thenaming right are independently and uniformly distributed over [0,100].There are several possible ideas to design the auction. a) The auction runs as follows. Both bidders are invited to the sameroom; an auctioneer will start the auction with an initial price 0, and increase it by $1 every minute. The bidders are not allowed to say anything during the process, but they can walk out of the room at any moment. If one bidder walks out of the room when the price increases to p (the bidder does not need to pay), the remaining bidder will be awarded the naming right for a price of p. If both walk out when the price reaches p, the naming right is not assigned and the two bidders do not need to pay. What should the bidders do? Explain your answer. (b) Both bidders are invited to submit their bids covertly (bids are non-negative real numbers).…A cool kid is willing to rename himself for a profit. He decides to auctionoff the naming right. Two bidders show interest. Their valuations for thenaming right are independently and uniformly distributed over [0,100].There are several possible ideas to design the auction. The auction runs as follows. Both bidders are invited to the same room; an auctioneer will start the auction with an initial price 0, and increase it by $1 every minute. The bidders are not allowed to say anything during the process, but they can walk out of the room at any moment. If one bidder walks out of the room when the price increases to p (the bidder does not need to pay), the remaining bidder will be awarded the naming right for a price of p. If both walk out when the price reaches p, the naming right is not assigned andthe two bidders do not need to pay. What should the bidders do? Explain your answer.Consider 5 bidders whose values are independently and uniformly distributed over [0, 900] (a) For a buyer with value 100, what is his equilibrium bid in a first-price auction (FPA)?
- What amount does each bidder bid in the Bayesian Nash equilibrium of a 2nd price auction? O The expected value of the second highest bidder. One half of the expected value of the second highest bidder. Their own value. One half of their own value.A cool kid is willing to rename himself for a profit. He decides to auctionoff the naming right. Two bidders show interest. Their valuations for thenaming right are independently and uniformly distributed over [0;100]:There are several possible ideas to design the auction. The auction runs as follows. Both bidders are invited to the sameroom; an auctioneer will start the auction with an initial price 0 and increase it by $1 every minute. The bidders are not allowed to say anything during the process, but they can walk out of the room at any moment. If one bidder walks out of the room when the price increases to p(the bidder does not need to pay), the remaining bidder will be awarded the naming right for a price of p. If both walk out when the price reaches p, the naming right is not assigned and the two bidders do not need to pay. What should the bidders do? Explain your answer.A cool kid is willing to rename himself for a profit. He decides to auctionoff the naming right. Two bidders show interest. Their valuations for thenaming right are independently and uniformly distributed over [0,100].There are several possible ideas to design the auction.(a) The auction runs as follows. Both bidders are invited to the sameroom; an auctioneer will start the auction with an initial price 0, and increase it by $1 every minute. The bidders are not allowed to say anything during the process, but they can walk out of the room at any moment. If one bidder walks out of the room when the price increases to p (the bidder does not need to pay), the remaining bidder will be awarded the naming right for a price of p. If both walk out when the price reaches p, the naming right is not assigned and the two bidders do not need to pay. What should the bidders do? Explain your answer. (b) Both bidders are invited to submit their bids covertly (bids are non-negative real…
- There are 3 bidders with valuations that are independently and uniformly distributed between 0 and 1. In equilibrium, what will Bidder 1 bid in a first-price auction if its valuation is 0.7? Round your answer to two decimal places.(a) Calculate the safety levels of both players.(b) Find the set of all Nash equilibria (pure and mixed).Suppose there are two bidders for a single object. Each bidder has a value for the object, v1 and v2, which is randomly drawn uniformly from 0 to 80. (Note that this means the probability that a value is 25 or lower is 25/80, and more generally, the probability that a value is k or lower is k/80). Bidders see their own values but not the values of their rival bidders. Consider a first price sealed bid auction where the winner of the object is the bidder who submits the highest bid and pays the price that he bid. Suppose that you are bidder 1 and you believe that your rival always bids a constant fraction α of his value. (For example, if bidder 2’ value is 15, he will bid 15α.). 1. What is your expected winning probability of the auction from any given bid b1? (You win the auction when your bid amount b1 is greater than your opponent’s bid). 2. What is your expected payoff from any given bid, b1? (Write answer as a function of v1, b1, and α). 3. Compute your best response bid given your…
- At an oral auction for a lamp, half of all bidders have a value of $50 and half have a value of $70. What is the expected winning bid if there are four bidders?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? %3DAssume that two collectors, X and Y are in a first prize sealed bid auction for a batch of vintage comic books. X and Y have different valuations (V) for this batch of comic books e.g. VX And VB are between $2000 and $4000. Both collectors know their own V but does not know the V of the other collector. All they know is that the other collector’s V is a uniformly distributed number between $2000 and $4000. Assume risk neutrality for X and Y e.g. expected payoff for X is: (VX – bX)Pr(bX) and expected payoff for Y is (VY – bY)Pr(bY). These collectors will make their bids strategically. Show how X’s bidding strategy is bX = ½ Vx + 1 and Y’s is bY = ½ Vy +1 in a Nash equilibrium.