Microeconomics
10th Edition
ISBN: 9781259655500
Author: David C Colander
Publisher: McGraw-Hill Education
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Question
Chapter 20, Problem 10QE
To determine
Roll back strategy of a player in a simultaneous move game.
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How do we solve a Sequential-move game?
Can a strategy be dominant for one player in a Nash equilibrium
Consider the following simultaneous move game:
Player 1
U
M
D
Player 2
L
2,10
2,5
8,7
C
5,2
11,8
8,4
R
5,4
2,9
8,3
In the Nash equilibrium of this game, player 1 receives a payoff of
✓ and player 2 receives a payoff of
Chapter 20 Solutions
Microeconomics
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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- Consider a sequential-move version of a rock-paper-scissor game. Players sequentially form one of three shapes with an outstretched hand. These shapes are "rock", "paper", and "scissors". A player playing rock will beat another player playing chosen scissors, but will lose to one playing paper; a play of paper will lose to a play of scissors. If both players choose the same shape, the game is tied. Suppose the winner receives a payoff of 1 and the loser receives the payoff of -1. Both players receive zero payoff under a tie. Suppose Player 1 moves first and Player 2 moves afterwards. In this game, what is the subgame perfect Nash equilibrium payoff of Player 1? 1 00 0-1arrow_forwardUse 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, 16arrow_forwardIn the game above, what is/are the EFFICIENT sub-game perfect Nash equilibrium?arrow_forward
- 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?arrow_forwardIf a game does not have an equilibrium in pure strategies, then it will not have an equilibrium in mixed strategies either. True or False?arrow_forwardThe following payoff matrix represents a simultaneous-move game between two players: Kay and Jack. Each player has two choices: Black or White. The first number in each cell is the payoff to Kay, and the second number is the payoff to Jack. Jay Black White 50, 30, Black 50 30 Кay 45, 40, White 30 50 Refer to the scenario above. Which is true? a. This game has a dominant strategy equilibrium. b. This game has two dominant strategy equilibria. c. This game has two Nash equilibria. d. This game has one Nash equilibrium.arrow_forward
- In a game of chicken, two drivers are heading towards each other on a collision course. The first one to swerve is considered the "chicken" and loses. What is the Nash equilibrium in this game? a) Both drivers swerve b) Neither driver swerves c) One driver swerves while the other doesn't d) It depends on the specificarrow_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_forwardRock-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_forward
- 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…arrow_forwardConsider a one-time game involving a penalty kick in football/soccer. There are two players: kicker and goalkeeper. The kicker has two possible actions: kick left or right. The goalkeeper also has two possible actions: guess left or right. The kicker and goalkeeper move simultaneously. If the kicker and goalkeeper choose the same direction, the goalkeeper "wins" and the payoffs are (0,1). If the kicker and goalkeeper choose different directions, the kicker wins and the payoffs are (1,0). (a) Is there a pure strategy equilibrium in this game? Explain. (b) Derive and explain the mixed strategy equilibrium for this game.arrow_forwardplease helparrow_forward
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