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 0 -1 rock paper 1 0 scissors -1 1 0 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 -3 paper 1 0 scissors -1 3 0 Suppose that we surtner alter the game from question 2 as follows: now whenever both players select the same strategy, both receive a payoff of 2. Note that this is no longer a zero-sum game. (a) Cin th off matrix fox this novel on ch
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 0 -1 rock paper 1 0 scissors -1 1 0 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 -3 paper 1 0 scissors -1 3 0 Suppose that we surtner alter the game from question 2 as follows: now whenever both players select the same strategy, both receive a payoff of 2. Note that this is no longer a zero-sum game. (a) Cin th off matrix fox this novel on ch
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:3.
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
paper 1
0
scissors -1 1
-1
0
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
1
0
rock
paper
scissors -1 3
-1
0
Suppose
that we nurtner alter the game from question 2 as follows: now whenever both
players select the same strategy, both receive a payoff of 2. Note that this is no
longer a zero-sum game.
(a) Give the payoff matrix for this game. As usual, you should list Rosemary's
payoffs first and Colin's payoffs second in each cell.
Underline the best responses for each player to each of the other players' strate-
gies in your payoff matrix. Then, find and give all Pure Nash equilibria for the
modified game.
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