Consider the 2-player, zero-sum game "Rock, Paper, Scissors". Each player choos 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
Consider the 2-player, zero-sum game "Rock, Paper, Scissors". Each player choos 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
Chapter15: Imperfect Competition
Section: Chapter Questions
Problem 15.7P
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6fe0f2e6-a3fe-44ed-a932-d5c5d1248f5a%2F2364b22a-1408-4d1b-b149-db6d2a5c5dc5%2Fsiu2b0e_processed.jpeg&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.
![2. Suppose now we alter the game so that whenever Colin chooses "paper" the loser
pays the winner 3 instead of 1:
I
rock paper scissors
rock
0
-3
1
paper
1
0
-1
scissors -1
3
0
(a) Show that x¹ = (3,3,3) and y¹ = (,) together are not a Nash equilibrium
for this modified game.
(b) Formulate a linear program that can be used to calculate a mixed strategy
x EA(R) that maximises Rosemary's security level for this modified game.
(c) Show that x¹ = (3,3,3) and y¹ = (,,) together are a Nash equilibrium for
this game](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6fe0f2e6-a3fe-44ed-a932-d5c5d1248f5a%2F2364b22a-1408-4d1b-b149-db6d2a5c5dc5%2F27w1m97_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Suppose now we alter the game so that whenever Colin chooses "paper" the loser
pays the winner 3 instead of 1:
I
rock paper scissors
rock
0
-3
1
paper
1
0
-1
scissors -1
3
0
(a) Show that x¹ = (3,3,3) and y¹ = (,) together are not a Nash equilibrium
for this modified game.
(b) Formulate a linear program that can be used to calculate a mixed strategy
x EA(R) that maximises Rosemary's security level for this modified game.
(c) Show that x¹ = (3,3,3) and y¹ = (,,) together are a Nash equilibrium for
this game
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