Managerial Economics: A Problem Solving Approach
5th Edition
ISBN: 9781337106665
Author: Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher: Cengage Learning
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Chapter 18, Problem 4MC
To determine
Winning bid.
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Hello, please help me to solve this question in Game Theory. Thanks in advance!Consider a first price sealed-bid auction of an object with two bidders. Each bidder i’s valuation of the object is vi, which is known to both bidders. The auction rules are that each player submits a bid in a sealed envelope. The envelopes are then opened, and the bidder who has submitted the highest bid gets the object and pays the auctioneer the amount of his bid. If the bidders submit the same bid, each gets the object with probability 0.5. Bids must be integers.
Find a Nash equilibrium for this game and show whether it is unique.
7.
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.
Chapter 18 Solutions
Managerial Economics: A Problem Solving Approach
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- Your company is bidding for mineral rights to a tract of land for drilling oil. Based on your geological survey reports, your valuation of the mineral rights is $38 million. You believe the distribution of bids will be uniform for the mineral rights, with a high value of $45 million and a low value of $20 million. In a second-price sealed-bid auction, how much should you for bid if there are 5 bidders? a. $41.40 Million O b. $45.00 Million Oc. $38.00 Million O d. $34.40 Millionarrow_forwardConsider the following situation: five individuals are participating in an auction for an old bicycle used by a famous cyclist. The table below provides the bidders' valuations of the cycle. The auctioneer starts the bid at an offer price far above the bidders' values and lowers the price in increments until one of the bidders accepts the offer. Bidder Value ($) 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?arrow_forwardPLEASE CHECK THIS HOW TO SOLVEarrow_forward
- 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.arrow_forwardQuestion is in the attachment section. Thank you in advance for your answer.arrow_forward• (1,0) (1,1) Player 2 G D H (2,0) Action Player 1 Player 1 Action B Player 1 (3,-1) E Player 2 (0,1) (-1,-1) (a) Find all the Subgame Perfect Nash equilibria in this game. (b) Find all the Nash equilibria in this game. (Hint: write the game in strategic form.)arrow_forward
- Nonearrow_forward4. 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.arrow_forwardSee attachmentsarrow_forward
- on 8.1 Consider the following game: Player 1 A C D 7,6 5,8 0,0 Player 2 E 5,8 7,6 1, 1 F 0,0 1,1 4,4 a. Find the pure-strategy Nash equilibria (if any). b. Find the mixed-strategy Nash equilibrium in which each player randomizes over just the first two actions. c. Compute players' expected payoffs in the equilibria found in parts (a) and (b). d. Draw the extensive form for this game.arrow_forward1. The following two examples show that truthful bidding is not a dominant strategy in the first- price and third-price auctions: a. Consider a first-price auction (The highest bidder wins the good, pays his or her bid; the other bidders do not pay). Suppose there are two bidders; bidder 1 has a value of 10. Argue that bidding 10 is not a best response for bidder 1 if bidder 2 bids 5. b. Consider a third-price auction (The highest bidder wins the good, pays the third highest bid; the other bidders do not pay). Suppose there are three bidders; bidder 1 has a value of 10. Argue that bidding 10 is not a best response for bidder 1 if bidder 2 bids 11 and bidder 3 bids 8.arrow_forwardExplain why the value of a matrix game is positive if all of the payoffs are positive. A. If the matrix game is strictly determined and all of the payoffs are positive, D=(a+d)−(b+c)will be negative and ad−bcwill be negative. Therefore, the value, v, will be positive. If the matrix game is nonstrictly determined, and all of the payoffs are positive, the saddle value will also be positive. Thus, the value, v, is positive. B. If the matrix game is strictly determined and all of the payoffs are positive, the saddle value will be negative. Thus, the value, v, is positive. If the matrix game is nonstrictly determined, D=(a+d)−(b+c) will be positive and ad−bc will be positive. Therefore, the value, v, will be positive. C. If the matrix game is strictly determined and all of the payoffs are positive, D=(a+d)−(b+c) will be positive and ad−bc will be positive. Therefore, the value, v, will be positive. If the matrix game is nonstrictly determined, and all of the…arrow_forward
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