Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN: 9781305506381
Author: James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher: Cengage Learning
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Chapter 15A, Problem 10E
To determine
To Ascertain: The bid amount that the former company can bid, based on the given information and the conditions.
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Consider the following three-player game represented in extensive form:
Player 3
L
Player 2
Player 1
R
Player 2
U
D
Player 3
(0,2,0)
U
D
U
D
(0, 1, 1)
(0, 3, k)
(0, 4, 3)
(0,4,2)
U
D
How many pure-strategy subgame-perfect Nash equilibria are there in this game if k > 1?
5
3
7
1
It depends on the value of k.
(2,2, 0)
Economics
Consider an infinitely repeated game played between two firms with the following payoffs (firm 1 is listed first):
· (250, 290) if both firms deviate
· (290, 330) if both firms cooperate
· (230, 370) if only firm 2 deviates
· (350, 270) if only firm 1 deviates
a. What probability-adjusted discount factor would ensure that Firm 1 would cooperate in a Nash equilibrium if Firm 2 applied a trigger strategy in the event that Firm 1 deviated?
b. What probability-adjusted discount factor would ensure that Firm 2 would cooperate in a Nash equilibrium if Firm 1 applied a trigger strategy in the event that Firm 2 deviated?
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 of…
Chapter 15A Solutions
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
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- In the normal form game below, the payoff matrix depends on the parameter a. 1 1 2 ABC a 0,2 6,4 -2,4 b 0, -24 -2a, 2a 8, 2 C 4,0 0,4 0, 14 Find the values of a, for which at least one pure strategy Nash equilibrium exists. Compute the value of a for which the expected payoff is the same for both players when the mixed strategy profile (01,02) = ((1/3,2/3,0), (0,1/4,3/4)) is played. Find the best response of player 1 (as a function of the parameter a) to player's 2 mixed strategy o2 = (1/2,1/2,0). Assuming a = 0 eliminate iteratively all dominated strategies and find a mixed strategy Nash equilibrium in this game.arrow_forwardThe Federal Communications Commission (FCC) has hired you as a consultant to design an auction to sell wireless spectrum rights. The FCC indicates that its goal of using auctions to sell these spectrum rights is to generate revenue. Since most bidders are large telecommunications companies, you rationally surmise that all participants in the auction are risk neutral. Which auction type—first-price, second-price, English, or Dutch—would you recommend if all bidders value spectrum rights identically but have different estimates of the true underlying value of spectrum rights?arrow_forwardq52 If you advertise and your rival advertises, you each will earn 14 million in profits. If neither of you advertises, you will each earn 20 million in profits. However, if one of you advertises and the other does not, the firm that advertises will earn 10 million and the non-advertising firm will earn 16 million. If you and your rival plan to be in business for only one year, the Nash equilibrium is a. for each firm to advertise. b. for the other firm to advertise and your firm not to advertise. c. for your firm to advertise and the other not to advertise. d. for neither firm to advertise.arrow_forward
- The Federal Communications Commission (FCC) has hired you as a consultant to design an auction to sell wireless spectrum rights. The FCC indicates that its goal of using auctions to sell these spectrum rights is to generate revenue. Since most bidders are large telecommunications companies, you rationally surmise that all participants in the auction are risk neutral. Which auction type—first-price, second-price, English, or Dutch—would you recommend if all bidders value spectrum rights identically but have different estimates of the true underlying value of spectrum rights? Kindly give a brief one-page description as part of the assignment.arrow_forwardIn the following symmetric general sum game (2, 2) (0,0) (0,0) (0,0) (0,0) (2, 2) (0,0) (2,2) (0,0) (i) Find all pure Nash equilibria. (ii) Find all mixed Nash equilibria in which all probabilities are positive. (vi) Which of these are evolutionary stable strategies?arrow_forwardThe FCC has hired you as a consultant to design an auction to sell wireless spectrum rights. The FCC indicates that its goal of using auctions to sell these spectrum rights is to generate revenue. Since most bidders are large telecommunications companies, you rationally surmise that all participants in the auction are risk neutral. Which auction type—first-price, second-price, English, or Dutch—would you recommend if all bidders value spectrum rights identically but have different estimates of the true underlying value of spectrum rights? Explainarrow_forward
- Consider the repeated game in which the following stage game is played twice in succession, with payoffs averaged between the two rounds (and no discounting). d e 0,0 b| 0,10 18, 18 48,10 10, 48 40, 40 a 4y, 4y 10,0 0,0 Set the parameter y equal to 1 (a) If (a, d) is played in the first period and (b, e) is played in the second period, what is the resulting (repeated game) payoff for the row player? (b) What is the highest payoff any player can receive in any subgame perfect Nash equilibrium of the repeated game?arrow_forwardDetermine all of the Nash equilibria (pure-strategy and mixed-strategy equilibria) of the following game:arrow_forwardConsider a Vickery auction. There are N bidders, each of them values the object £vi, with i = 1…N. Each bidder can submit a bid in a sealed envelope. Once all the bids have been made, the envelopes are opened. The winner of the auction is the bidder who made the highest bid, however, s/he pays the second-highest bid. What are the weakly dominant strategies in this game? Is there only one?arrow_forward
- The Government of Malaca has decided to sell pollution permits that will allow people to discharge pollutants into its largest freshwater lake. Each permit represents the right to discharge one tonne of pollutants. Malaca has determined that the lake will tolerate a maximum of 40 tonnes of pollutants per year and has decided to sell the permits using a Dutch auction. This means that the auction starts at a very high price, which is reduced in steps until the price reaches a level that will result in all 40 tonnes of pollution permits being sold at the same price. The results of the bidding are shown in table below. Price per PollutionPermit BidderA BidderB BidderC BidderD BidderE $5,500 2 5,000 4 6 4,500 6 6 1 1 1 4,000 8 7 2 2 2 3,500 10 7 4 3 3 3,000 12 9 6 3 4 2,500 14 10 8 3 5 2,000 16 11 9 4 6 1,500 18 12 10 4 7 a. What will be the price of pollution permits as a result of this auction? Price: $ b. Suppose that Bidder E happened to be an…arrow_forwardThe Government of Malaca has decided to sell pollution permits that will allow people to discharge pollutants into its largest freshwater lake. Each permit represents the right to discharge one tonne of pollutants. Malaca has determined that the lake will tolerate a maximum of 10 tonnes of pollutants per year and has decided to sell the permits using a Dutch auction. This means that the auction starts at a very high price, which is reduced in steps until the price reaches a level that will result in all 10 tonnes of pollution permits being sold at the same price. The results of the bidding are shown in table below. Price per Pollution Bidder Bidder Bidder Bidder Bidder Permit A. B D $5, 500 1 5,000 4,500 4,000 1. 1. 1 2 2. 3 2 1 2 3,500 3,000 2,500 2,000 4 3 2 4 4 4 3 4 4 1,500 7 a. What will be the price of pollution permits as a result of this auction? Price: $ b. Suppose that Bidder E happened to be an environmental protection group. If this group had not participated in the…arrow_forwardConsider this "all-pay" auction in which the highest bidder wins and both bidders must pay an amount equal to their bid regardless of whether they win or lose. It is common knowledge that Bidder 1 has a valuation of 2 and Bidder 2 has a valuation of 3. The bids must be whole numbers and Bidder 2 wins in the event of tie. Which of the following are Nash equilibria? Bidder 2 1 2 3 4 0, 3 0, 2 0, 1 0,0 0, -1 1 1,0 -1, 2 -1, 1 -1, 0 -1, -1 Bidder 1 2 0,0 О, -1 -2, 1 -2, 0 -2, -1 3 -1, 0 -1, -1 -1, -2 -3, 0 -3, -1 4 -2, 0 -2, -1 -2, -2 -2, -3 -4, -1 Note: The notation [0], [1], etc. denotes the pure strategies in which the bidder bids 0,1, etc. Mixed strategies are represented by weighted averages of the pure strategies, e.g the mixed strategy in which a bidder bids 1 with a probability of 1/4 and 4 with a probability of 3/4 is written as 1/4 [1] + 3/4 [4]. O ([0], [3]) O ([0], [1]) O ((1], [O]) (5/12 [0] + 1/3 [1] + 1/4 [2], 1/2 [0] + 1/2 [1]) O (2/3 [0] + 1/3 [1], 1/2 [0] + 1/2 [1]) O…arrow_forward
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