4. Consider a game of rock, paper and scissors: 2 P S -2,2 3,-3 0,0 -1,1 S-3,3 1,-1 0,0 R 1 P R 0,0 2,-2 Notice that the payoffs differ from those of the rock, paper and scissors example shown in class. You can interpret then as follows: Players always like to win, but winning with rock (against scissors) is better than winning with paper (against rock), which is better than winning with scissors (against paper). I honestly think that these payoffs make a lot of sense. Which of the statements below is correct about this game? (a) The Nash equilibrium in mixed strategies of this game consists of each player playing R with probability; P with probability; and S with probability 12. (b) The Nash equilibrium in mixed strategies of this game consists of each player playing R with probability ; P with probability ; and S with probability 3. (c) The Nash equilibrium in mixed strategies of this game consists of each player playing R with probability 12; P with probability; and S with probability 12. (d) The Nash equilibrium in mixed strategies of this game consists of each player playing R with probability ; P with probability 3; and S with probability 2.
4. Consider a game of rock, paper and scissors: 2 P S -2,2 3,-3 0,0 -1,1 S-3,3 1,-1 0,0 R 1 P R 0,0 2,-2 Notice that the payoffs differ from those of the rock, paper and scissors example shown in class. You can interpret then as follows: Players always like to win, but winning with rock (against scissors) is better than winning with paper (against rock), which is better than winning with scissors (against paper). I honestly think that these payoffs make a lot of sense. Which of the statements below is correct about this game? (a) The Nash equilibrium in mixed strategies of this game consists of each player playing R with probability; P with probability; and S with probability 12. (b) The Nash equilibrium in mixed strategies of this game consists of each player playing R with probability ; P with probability ; and S with probability 3. (c) The Nash equilibrium in mixed strategies of this game consists of each player playing R with probability 12; P with probability; and S with probability 12. (d) The Nash equilibrium in mixed strategies of this game consists of each player playing R with probability ; P with probability 3; and S with probability 2.
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.9P
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Question
Transcribed Image Text:4. Consider a game of rock, paper and scissors:
2
R
P
S
R
0,0 -2,2 3,-3
1 P 2,-2 0,0 −1,1
S-3,3 1,−1 0,0
Notice that the payoffs differ from those of the rock, paper and scissors example shown
in class. You can interpret then as follows: Players always like to win, but winning
with rock (against scissors) is better than winning with paper (against rock), which is
better than winning with scissors (against paper). I honestly think that these payoffs
make a lot of sense. Which of the statements below is correct about this game?
12*
(a) The Nash equilibrium in mixed strategies of this game consists of each player
playing R with probability 12; P with probability; and S with probability 22.
(b) The Nash equilibrium in mixed strategies of this game consists of each player
playing R with probability ; P with probability ; and S with probability.
(c) The Nash equilibrium in mixed strategies of this game consists of each player
playing R with probability ; P with probability 5; and S with probability 12.
(d) The Nash equilibrium in mixed strategies of this game consists of each player
playing R with probability ; P with probability; and S with probability 21.
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