MICROECONOMICS-ACCESS CARD <CUSTOM>
11th Edition
ISBN: 9781266285097
Author: Colander
Publisher: MCG CUSTOM
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Question
Chapter 20.1, Problem 2Q
To determine
The strategy of B when A confesses.
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Suppose that you and a friend play a matching pennies game in which each of you
uncovers a penny. If both pennies show heads or both show tails, you keep both. If one shows
heads and the other shows tails, your friend keeps them. Show the pay- off matrix. What, if
any, is the pure-strategy Nash equilibrium to this game? Is there a mixed-strategy Nash
equilibrium? If so, what is it?
Use the following payoff matrix for a simultaneous-move one-shot game to answer the accompanying questions.
Player 1
Strategy
C
15, 7
8, 12
a. What is player 1's optimal strategy?
Player 1 does not have an optimal strategy.
Strategy A.
Strategy B.
b. Determine player 1's equilibrium payoff.
Player 2
D
10, 11
19,
7
E
19, 15
12, 3
F
18, 20
15, 16
CLASSES OF GAMES
First, Alice chooses either action al or action a2. If Alice chooses action al, then she receives a payoff of 2 and Bob receives a payoff of 8. If Alice chooses
action a2, then Bob chooses either action b1 or action b2. If Bob chooses action b1, then Alice receives a payoff of 0 and Bob receives a payoff of 2. If
Bob chooses action b2, then Alice receives a payoff of 4 and Bob receives a payoff of 4.
Which of the following are correct statements about the game described in the previous paragraph? (Mark all that are correct.)
This game has perfect information.
The strategy profile (a2,b1) is a Nash equilibrium of this game.
Bob's backward induction payoff is 8.
The strategy profile (al,b1) is a Nash equilibrium of this game.
The strategy profile (a1,b2) is a Nash equilibrium of this game.
The strategy profile (a2,b2) is a Nash equilibrium of this game.
This is a bargaining game.
This is a promise game.
This is a threat game.
Alice's backward induction payoff is 2.
Chapter 20 Solutions
MICROECONOMICS-ACCESS CARD <CUSTOM>
Ch. 20.1 - Prob. 1QCh. 20.1 - Prob. 2QCh. 20.1 - Prob. 3QCh. 20.1 - Prob. 4QCh. 20.1 - Prob. 5QCh. 20.1 - Prob. 6QCh. 20.1 - Prob. 7QCh. 20.1 - Prob. 8QCh. 20.1 - Prob. 9QCh. 20.1 - Prob. 10Q
Ch. 20.A - Netflix and Hulu each expects profit to rise by...Ch. 20.A - Prob. 2QECh. 20 - Prob. 1QECh. 20 - Prob. 2QECh. 20 - Prob. 3QECh. 20 - Prob. 4QECh. 20 - Prob. 5QECh. 20 - Prob. 6QECh. 20 - Prob. 7QECh. 20 - Prob. 8QECh. 20 - Prob. 9QECh. 20 - Prob. 10QECh. 20 - Prob. 11QECh. 20 - Prob. 12QECh. 20 - Prob. 13QECh. 20 - Prob. 14QECh. 20 - Prob. 15QECh. 20 - Prob. 16QECh. 20 - Prob. 1QAPCh. 20 - Prob. 2QAPCh. 20 - Prob. 3QAPCh. 20 - Prob. 4QAPCh. 20 - Prob. 5QAPCh. 20 - Prob. 6QAPCh. 20 - Prob. 1IPCh. 20 - Prob. 2IPCh. 20 - Prob. 3IPCh. 20 - Prob. 4IPCh. 20 - Prob. 5IPCh. 20 - Prob. 6IPCh. 20 - Prob. 7IP
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- Use the following payoff matrix to answer the questions below. Cooperate Defect 1 Cooperate 100, 100 40, 125 Defect 125, 40 50, 50 Which player (if any) has a Dominant Strategy? [ Select ] What is the Nash Equilibrium of this game? [ Select ] Does this game satisfy the definition of a prisoner's dilemma? [ Select ]arrow_forwardAlice chooses action a or action b, and her choice is observed by Bob. If Alice chooses action a, then Alice receives a payoff of 5 and Bob receives a payoff of 7. If Alice chooses action b, then Bob chooses action cor action d. If Bob chooses action c, then Alice receives a payoff of 10 and Bob receives a payoff of 5. If Bob chooses action d, then Alice receives a payoff of 0 and Bob receives a payoff of 3. Which of the following are correct statements about the game described in the previous paragraph? (Mark all that are correct.) O This game has imperfect information. O Alice's backward induction payoff is 5. O This is a promise game. O Alice's backward induction payoff is 0. O This is a prisoners' dilemma. O Bob's backward induction payoff is 5. O Bob's backward induction payoff is 3. O This is a threat game.arrow_forwardWhich of the following best defines a Nash Equilibrium? A) A situation where each player maximizes their own payoff without regard to the strategies of others. B) A situation where no player can improve their payoff by unilaterally changing their strategy. C) A situation where players cooperate to achieve the highest collective payoff. D) A situation where each players strategy maximizes the opponents payoff.arrow_forward
- Please can you redraw the payoff matrixarrow_forwardConsider 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_forwardWhich player (if any) has a dominate strategy? What is the Nash Equilibrium of this game? Does the game satisfy the definition of prisoner dilemma?arrow_forward
- 1) Suppose that Player A can take two actions, either Up or Down. Player A is thinking to choose Up 50 percent of the time, and Down 50 percent of the time. This type of strategy is called a ____ ? 2) Consider a payoff matrix of a game shown below. In each cell, the number on the left is a payoff for Player A and the number on the right is a payoff for Player B. In order for (Down, Right) to be a unique pure strategy Nash equilibrium, a must be (greater, or smaller) than 3 and b must be (greater, or smaller) than 3. refer to imagearrow_forwardRefer to the accompanying payoff matrix. Which of the following is a Nash equilibrium? Company A Strategy 1 Strategy 2 Strategy 1 Company A's Profit: $8 million Company B's Profit: $9 million Company B Company A's Profit: $10 million Company B's Profit: $8 million None of the above, Strategy 2 Company B's Profit: $8 million Company A's Profit: $7 million Company B's Profit: $7 million Company A's Profit: $8 million Company A chooses Strategy 1 and Company B chooses Strategy 1. Company A chooses Strategy 2 and Company B chooses Strategy 2. Company A chooses Strategy 1 and Company B chooses Strategy 2. Company A chooses Strategy 2 and Company B chooses Strategy 1.arrow_forwardDesign the payoffff matrix of a game with no Nash Equilibria. The game should have 2 players, 2 strategies for each player, and the payoffffs for each player should be either 0 or 1.arrow_forward
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