Economics: Principles & Policy
14th Edition
ISBN: 9781337696326
Author: William J. Baumol; Alan S. Blinder; John L. Solow
Publisher: Cengage Learning
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Question
Chapter 13, Problem 3TY
To determine
Payoff matrix.
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a.
b.
Each firm has four alternative strategies, and a certain profit/payoff is associated with
each strategy. The numbers in the payoff matrix denote firm A's profit (in thousands of
dollars). The total amount of profit that can be earned by the two firms together is
$20000. (This is called a "constant sum game.") Firm B's profit is therefore $20000
minus firm A's profit. What strategies will the two firms select? Is the game strictly
determined? If so, how much does each firm gain?
B's strategies
A's strategies ↓
Increase
Advertising
Decrease
Price
Increase
Price
Alter
Product
Increase
Advertising
0
11
8
11
Decrease
Price
8
10
6
2
Increase
Price
7
12
15
Alter
Product
4
15
3
12
Suppose now that due to a change in consumer preferences, firm A's "Increase Price"
strategy pays off better than before when firm B elects to "Decrease Price," that is, the
payoff rises from 6 to 14. What strategies will the two firms now select? Is the game
strictly determined? If so, how much does each firm…
The following payoff matrix represents a simultaneous-move game between two players: John and Trevor. Each player has to choices:
Black or White. The first number in each cell is the payoff to John, and the second number is the payoff to Trevor.
Trevor
Black
White
Black
15, 15
10, 10
John
White
12, 10
13, 15
Refer to the table above. Which statement is true?
a. Neither John nor Trevor have a dominant strategy in this game.
b. Only Trevor has a dominant strategy in this game.
c. Only John has a dominant strategy in this game.
d. John and Trevor both have a dominant strategy in this game.
Three married couples in the state of Maryland—Bob and Carol, Ted and Alice, and Ross and Mike (remember, same-sex marriage is legal in the state of Maryland)—are thinking about renting a boat to go sailing on the Chesapeake Bay. The cost of a boat rental is $600. Each of the three couples puts some amount of money in an envelope. Thus, each player in this game is a couple. If the total amount collected is at least $600, then the boat is rented. If the amount collected is more than $600, then the money left over after renting the boat is spent on wine. If the total amount collected is less than $600, then they do not rent the boat, and the money is spent on a dinner. Assume the benefit to a couple from the boat trip is 400, the benefit from each dollar spent on wine is 50 cents, the benefit from each dollar spent on dinner is 40 cents, and the personal cost of the contribution to a couple equals the amount of contribution. For example, if the boat is rented, $50 of wine is purchased…
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Similar questions
- Consider a sequential game where there are two players, Jake and Sydney. Jake really likes Sydney and is hoping to run in to her at a party this weekend. Sydney can't stand Jake. There are two parties going on this weekend and each player's payoffs are a function of whether they see one another at the party. The payoff matrix is as follows: Sydney Party 1 Party 2 Party 1 6, 18 18, 6 Jake Party 2 24,8 0,24 a) Does this game have a pure strategy Nash Equilibrium? b) What is the mixed strategy Nash Equilibrium? c) Now suppose Sydney decides what party she is going to first. Her roommate is friends with Jake and will call him to tell him which party they go to. Write the extensive form of this game (game tree). d) What is the subgame perfect Nash equilibrium from part c?arrow_forwardImagine United Airlines deciding independently to reduce fares on its flights. Other competing airlines quickly matched the fare cuts. These actions might be interpreted as: a cooperative game. a competitive game. a constant sum game. a noncooperative game.arrow_forwardBob's Product- Strategy Pizza No Pizza Sam's Product Strategy No Pizza A U Pizza -$10 с -$10 $0 $15 B D $15 $10 $0 $10 Refer to the payoff matrix. Bob's Burgers and Sam's Sandwiches are competing restaurants in a small town. Both are considering adding pizza to their line of products. If this is a sequential game but we don't know who moves first, what can we say about the final outcome? A. There is no Nash equilibrium attainable for this game. B. Cell A represents the only Nash equilibrium possible for this game. C. Cell D represents the only Nash equilibrium possible for this game. D. Cells B and C both represent possible Nash equilibrium outcomes for this game.arrow_forward
- Rock-paper-scissors is a game in which players typically use mixed strategies. Can you think of other examples? What are some of the characteristics of games that usually involve playing mixed strategies?arrow_forwardTwo players, Player 1 and Player 2, are playing a repeated prisoner's dilemma. Payoffs are described in the following matrix. Answer which statement is correct: Player 2 A B Player 1 A 10, 10 1,150 B 150, 1 2,2 Select one: a. A tit-for-tat strategy will support (A,A) as an equilibrium if 8 > 0.7 ○ b. A tit-for-tat strategy will C. ○ d. d. never support (A,A) as an equilibrium. A trigger strategy will never support (A,A) as an equilibrium. A trigger strategy will support (A,A) as an equilibrium if 8 > 0.7arrow_forwardConsider the following game: Mercedes-Benz and Honda are the only two firms in the market for automobiles. Each firm has two strategies: produce high-grade vehicles or produce low-grade vehicles. The first entry in the bracket is the payoffs (in $billion) of Mercedes-Benz and the second entry is the payoffs of Honda. (see the image) What is the dominant strategy of Mercedes-Benz and Honda? Also, what is the Nash equilibrium of this game?arrow_forward
- Which of the following is true for a two-person game which has a Nash equilibrium? The game may or may not have a dominant-strategy equilibrium. Only one of the two players will have a dominant strategy. The game must have a dominant-strategy equilibrium. The dominant strategy of the players must be different.arrow_forwardConsider the following payoff matrix below. Player 1 and Player 2 have two options, A or B. The payoffs are given in the form of (Player 1, Player 2). Higher numbers are more desirable. What is Player 2's dominant strategy? Player 2 B A Player 1 A 5,6 2,2 B 4,3 5,2 O Play A Play B O No Dominant Strategyarrow_forwardSuppose there are two farmers, each of whom has the right to graze cows on the village common. Denote by sA and sB the number of cows farmers A and B graze, respectively. The payoff per cow is given by 120-sA-sB and farmers decide on the number of cows they will graze on the common simultaneously (a) Formulate this situation as a strategic game and find the Nash equilibrium (b) Compare the equilibrium farmer profits to those that would have been realized if each farmer grazed 30 cows on the village common. Explainarrow_forward
- Consider a two-person zero-sum game where the payoff listed below are the winnings for Company X. The given payoff matrix is: Company Y Strategies Company X Strategies y1 y2 y3 x1 3 5 9 x2 8 4 3 x3 7 6 7 Identify the pure strategy solution. What is the value of the gamearrow_forwardQuestion 3: Represent Rock-Paper-Scissors 1 point, the loser gets -1 and in case of a tie each player gets 0. What are the dominant strategies? What is the Nash equilibrium? game in a matrix format. Note that the winner getsarrow_forward1.9. What is a mixed strategy in a normal-form game? What is a mixed-strategy Nash equilibrium in a normal-form game?arrow_forward
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