2. (Second-price auction) Consider the second price auction in the independent private values framework. The reserve price is 0, so the object is always sold. Two bidders i=1,2 have independent, uniformly drawn valuations ~ U[0, 1] and simultaneously place bids by. The winner is the highest bidder, but the price paid is the bid of the second bidder. The loser gets nothing. To summarize: if by > b2, payoffs are (v1-b2, 0). If by

2. (Second-price auction) Consider the second price auction in the independent private values framework. The reserve price is 0, so the object is always sold. Two bidders i=1,2 have independent, uniformly drawn valuations ~ U[0, 1] and simultaneously place bids by. The winner is the highest bidder, but the price paid is the bid of the second bidder. The loser gets nothing. To summarize: if by > b2, payoffs are (v1-b2, 0). If by

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter18: Asymmetric Information

Section: Chapter Questions

Problem 18.10P

See similar textbooks

Similar questions

4 A recently discovered painting by Picasso is on auction at Sotheby's. There are two main bidders Amy and Ben {1,2}. Bidding starts at £10M but the value of the painting is certainly not more than £20M. Each bidder's valuation v; is independently and uni- formly distributed on the interval [10M, 20M], and this is common knowledge among the players: A bidder knows their own valuation but not of their opponent. Consider an auction where an object is allocated to the highest bidder but the price paid by the bidder is determined randomly. With probability 3/4, the bidder pays their own bid, and with probability 1/4 the bidder pays the losing bid. The person bidding lowest pays nothing. If the bids are equal, each bidder gets the object with probability one-half, and in this case, pays their bid. Suppose that bidder 1 assumes that bidder 2 will bid a constant fraction, 7, of bidder 2's valuation (and similarly, bidder 2 assumes bidder 1 will bid the same constant propor- tional value y of…
Typed Plzzz And Asap thanks
4. A uniform price auction is an auction where all the winners pay the same price. A k-th price auction is an auction where the price paid by the winner(s) is the k-th highest bid. We run a 3rd price, uniform price auction for two items, so the winners are the two bidders with the highest bid. There are 4 bidders, A, B, C and D, and they bid respectively $10, $9, $8 and $12. (A) Bidders A and B win the auction and pay $9. (B) Bidders A and D win the auction and pay $9. (C) Bidders B and D win the auction and pay $10. (D) Bidders B and C win the auction and pay $8.
5.
2. Consider the following two player game in normal form: Player 2 R 0, 5 2, 3 2, 3 Player 1 M 2, 3 0, 5 3, 2 B 5,0 3, 2 2, 3 (a) Show that for Player 1, strategy T is strictly dominated by a mixed strategy in which actions M and B are played with positive probability. (b) Find a mixed strategy Nash equilibrium of this game. 352
4 Problem: Ticket Exchange Each of two players draw a lottery ticket with a random prize written on it. You can assume that prizes a uniformly drawn from an interval between 0 and 100 (can you solve it without uniform assumption?). Both player simultaneously decide whether to keep the prize or exchange the ticket with another player. If both decide to exchange, then the tickets are swapped and each player collects a prize from the newly acquired ticket. Find the BNE of the game. Hint: consider cut-off strategies, i.e. that prizes above some x are kept, and below z are offered for exchange.
2. Consider a similar auction problm as before. Two firms compete for a contract to build a university building. Their construction costs are independent and uniformly drawn from [0,1]. (a) Suppose the auction is conducted as follows. Price starts at 1 (at this price both bidders would be happy to win the project). The price goes down continuously: at time t = [0, 1], the price will be 1 - t. At any time t, any bidder can shout "floccinaucinihilipilificious." Once that happens, the price will stop to decline. The bidder who remains silent becomes the winner and he is paid the price at that moment. If both players say it at the same time, the auction ends without a winner. If no player speaks until t = 1 (and the price will be zero by then), the game ends and a winner is selected randomly for a price of 0. Analyze this auction. You don't have to provide rigorous mathematical proofs. How does this auction relate to (a) or (b)?
2. Consider a similar auction problm as before. Two firms compete for a contract to build a university building. Their construction costs are independent and uniformly drawn from [0, 1]. (a) Suppose the auction is conducted as follows. Price starts at 1 (at this price both bidders would be happy to win the project). The price goes down continuously: at time t = [0, 1], the price will be 1- t. At any time t, any bidder can shout "floccinaucinihilipilificious." Once that happens, the price will stop to decline. The bidder who remains silent becomes the winner and he is paid the price at that moment. If both players say it at the same time, the auction ends without a winner. If no player speaks until t = 1 (and the price will be zero by then), the game ends and a winner is selected randomly for a price of 0. Analyze this auction. You don't have to provide rigorous mathematical proofs. How does this auction relate to (a) or (b)? 1 (b) Suppose the auction is conducted as follows. Price…
3. Suppose Chelsea has the following utility function over wealth: v (y) = ln y (a) Show that Chelsea is risk averse. (b) Consider the lottery that yields the outcome $2 with probability ; and the outcome $8 with probability . How much money would you need to offer Chelsea to buy the lottery from her if the lottery is all she owns? (c) What is the Chelsea's risk premium for this lottery? (d) Suppose Antonio has utility function over wealth given by Va (y) = Vy and suppose Dillon has the following utility function over wealth: Va (y) = In Vy Who is more risk averse, Antonio or Dillon? Show this using two approaches. (e) Who is more risk averse, Chelsea or Dillon? Explain.
6. Nash Bargaining Players 1 and 2 bargain over how to split a pie of size 1. Suppose the players simultaneously announce how much of the pie they claim for themselves. Let x; denote the claim of player i e {1,2}. Claims have to satisfy 0 1, then neither player gets anything. Suppose that each player's utility is strictly increasing in the amount of pie she gets. Find all Nash equilibria.
4. A decision-maker faces a lottery that gives her a final wealth of 1 dollar with probability 1/4, 3 dollars with probability 1/2, and 8 dollars with probability 1/4. (a) Suppose this decision-maker is an expected utility maximizer with von Neumann-Morgenstern utility u₁(x) = √x+1, where z is her final wealth. Find the risk premium associated with this lottery. Solution: The expected value of the lottery is 1/4+3/2+8/4 = 15/4. The certainty equivalent, CE, solves √CE+1= √2 √4 √9 7+√2 + Hence CE = (35+ 14√2)/16 and the risk premium is (25-14√/2)/16. (b) Now suppose that a second decision-maker who maximizes expected utility with von Neumann-Morgenstern utility u₂(x) = √faces the same lottery. Without calculating this decision-maker's risk premium, determine whether it is higher than, lower than, or the same as that for the decision-maker in part (a). Solution: The first decision-maker has Arrow-Pratt measure u₁(x) 1 u₁(x) 2(x + 1) r₁(x) = and the second has Arrow-Pratt measure r₂(x):…
5.q1