Consider the 2-player, zero-sum game "Rock, Paper, Scissors". Each player choosesone 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 choosesscissors, 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:rockpaper scissorsrock 0-11paper10scissors -1 1-102. Suppose now we alter the game so that whenever Colin chooses "paper" the loserpays the winner 3 instead of 1:rock paper scissors0 -30-1 3rockpaper 1scissors-10(e) Show that x¹ = () and y¹ = (₁) together are a Nash equilibrium forthis game.

In game theory, a Nash equilibrium is a set of strategies where each player's strategy is the best…

Answered: (e) Show that x¹=(..) and y¹ = (3. 4. )…

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(e) Show that x¹=(..) and y¹ = (3. 4. ) together are a Nash equilibrium for this game.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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.
We can write the payoff matrix for this game as follows:
rock
paper scissors
rock 0
-1
1
paper
1
0
scissors -1 1
-1
0
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
0 -3
0
-1 3
rock
paper 1
scissors
-1
0
(e) Show that x¹ = () and y¹ = (₁) together are a Nash equilibrium for
this game.

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