Consider the 2-player, zero-sum game "Rock, Paper, Scissors". Each player chooses one of 3 strategies: rock, paper, or scissors. Then, both players reveal their choices. The outcome is determined as follows. If both players choose the same strategy, neither player wins or loses anything. Otherwise: "paper covers rock": if one player chooses paper and the other chooses rock, the player who chose paper wins and is paid 1 by the other player. "scissors cut paper": if one player chooses scissors and the other chooses paper, the player who chose scissors wins and is paid 1 by the other player. • "rock breaks scissors": if one player chooses rock and the other player chooses scissors, the player who chose rock wins and is paid 1 by the other player. We can write the payoff matrix for this game as follows: scissors rock paper -1 rock 0 paper 1 0 scissors -1 1 -1 2. Suppose now we alter the game so that whenever Colin chooses "paper" the loser pays the winner 3 instead of 1: rock paper scissors -3 1 rock 0 paper 1 0 scissors (a) Show that x¹=(.) and yT=(..) together are not a Nash equilibrium for this modified game.
Consider the 2-player, zero-sum game "Rock, Paper, Scissors". Each player chooses one of 3 strategies: rock, paper, or scissors. Then, both players reveal their choices. The outcome is determined as follows. If both players choose the same strategy, neither player wins or loses anything. Otherwise: "paper covers rock": if one player chooses paper and the other chooses rock, the player who chose paper wins and is paid 1 by the other player. "scissors cut paper": if one player chooses scissors and the other chooses paper, the player who chose scissors wins and is paid 1 by the other player. • "rock breaks scissors": if one player chooses rock and the other player chooses scissors, the player who chose rock wins and is paid 1 by the other player. We can write the payoff matrix for this game as follows: scissors rock paper -1 rock 0 paper 1 0 scissors -1 1 -1 2. Suppose now we alter the game so that whenever Colin chooses "paper" the loser pays the winner 3 instead of 1: rock paper scissors -3 1 rock 0 paper 1 0 scissors (a) Show that x¹=(.) and yT=(..) together are not a Nash equilibrium for this modified game.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
![Consider the 2-player, zero-sum game "Rock, Paper, Scissors". Each player chooses
one of 3 strategies: rock, paper, or scissors. Then, both players reveal their choices.
The outcome is determined as follows. If both players choose the same strategy,
neither player wins or loses anything. Otherwise:
"paper covers rock": if one player chooses paper and the other chooses rock,
the player who chose paper wins and is paid 1 by the other player.
"scissors cut paper": if one player chooses scissors and the other chooses paper,
the player who chose scissors wins and is paid 1 by the other player.
"rock breaks scissors": if one player chooses rock and the other player chooses
scissors, the player who chose rock wins and is paid 1 by the other player.
We can write the payoff matrix for this game as follows:
rock paper scissors
rock 0
paper 1 0
scissors
2. Suppose now we alter the game so that whenever Colin chooses "paper" the loser
pays the winner 3 instead of 1:
rock paper scissors
rock 0
paper 1
scissors
-3
0
3
(a) Show that x¹ = (-) and y¹ = (4) together are not a Nash equilibrium
for this modified game.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8d1b97ca-a014-4a9d-850a-b61b08d119c0%2F28891c7e-d789-41d2-98e6-b7c7d091c396%2Fk5lvvrn_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the 2-player, zero-sum game "Rock, Paper, Scissors". Each player chooses
one of 3 strategies: rock, paper, or scissors. Then, both players reveal their choices.
The outcome is determined as follows. If both players choose the same strategy,
neither player wins or loses anything. Otherwise:
"paper covers rock": if one player chooses paper and the other chooses rock,
the player who chose paper wins and is paid 1 by the other player.
"scissors cut paper": if one player chooses scissors and the other chooses paper,
the player who chose scissors wins and is paid 1 by the other player.
"rock breaks scissors": if one player chooses rock and the other player chooses
scissors, the player who chose rock wins and is paid 1 by the other player.
We can write the payoff matrix for this game as follows:
rock paper scissors
rock 0
paper 1 0
scissors
2. Suppose now we alter the game so that whenever Colin chooses "paper" the loser
pays the winner 3 instead of 1:
rock paper scissors
rock 0
paper 1
scissors
-3
0
3
(a) Show that x¹ = (-) and y¹ = (4) together are not a Nash equilibrium
for this modified game.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.Recommended textbooks for you
![ENGR.ECONOMIC ANALYSIS](https://compass-isbn-assets.s3.amazonaws.com/isbn_cover_images/9780190931919/9780190931919_smallCoverImage.gif)
![Principles of Economics (12th Edition)](https://www.bartleby.com/isbn_cover_images/9780134078779/9780134078779_smallCoverImage.gif)
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
![Engineering Economy (17th Edition)](https://www.bartleby.com/isbn_cover_images/9780134870069/9780134870069_smallCoverImage.gif)
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
![ENGR.ECONOMIC ANALYSIS](https://compass-isbn-assets.s3.amazonaws.com/isbn_cover_images/9780190931919/9780190931919_smallCoverImage.gif)
![Principles of Economics (12th Edition)](https://www.bartleby.com/isbn_cover_images/9780134078779/9780134078779_smallCoverImage.gif)
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
![Engineering Economy (17th Edition)](https://www.bartleby.com/isbn_cover_images/9780134870069/9780134870069_smallCoverImage.gif)
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
![Principles of Economics (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305585126/9781305585126_smallCoverImage.gif)
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
![Managerial Economics: A Problem Solving Approach](https://www.bartleby.com/isbn_cover_images/9781337106665/9781337106665_smallCoverImage.gif)
Managerial Economics: A Problem Solving Approach
Economics
ISBN:
9781337106665
Author:
Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:
Cengage Learning
![Managerial Economics & Business Strategy (Mcgraw-…](https://www.bartleby.com/isbn_cover_images/9781259290619/9781259290619_smallCoverImage.gif)
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education