GATE 2024 Question 45: Game theory and strategic behaviour
Two friends Aditi and Raju are deciding independently whether to watch a movie or go to a music concert that evening. Both friends would prefer to spend the evening together than apart. Aditi would prefer that they watch a movie together, while Raju would prefer that they go to the concert together. The payoff matrix arising from their actions is presented below. p and (1−p) are the probabilities that Aditi will decide in favour of the movie and concert, respectively. Similarly, q and (1−q) are the probabilities that Raju will decide in favour of the movie and concert, respectively. Which one of the following options correctly contains all the Nash Equilibria?
Raju: Movie
Raju: Concert
Aditi: Movie
2,1
0,0
Aditi: Concert
0,0
1,2
Tap an option to check your answer.
Answer and worked solution
Checking your account…
Plain-text version
Two friends Aditi and Raju are deciding independently whether to watch a movie or go to a music concert that evening. Both friends would prefer to spend the evening together than apart. Aditi would prefer that they watch a movie together, while Raju would prefer that they go to the concert together. The payoff matrix arising from their actions is presented below. p and (1-p) are the probabilities that Aditi will decide in favour of the movie and concert, respectively. Similarly, q and (1-q) are the probabilities that Raju will decide in favour of the movie and concert, respectively. Which one of the following options correctly contains all the Nash Equilibria? | Raju: Movie | Raju: Concert | Aditi: Movie | 2,1 | 0,0 | Aditi: Concert | 0,0 | 1,2 | (A) (p=0,q=0); (p=1,q=1); (p=2/3,q=1/3) (B) (p=0,q=1); (p=1,q=0); (p=2/3,q=1/3) (C) (p=0,q=0); (p=1,q=1); (p=1/3,q=2/3) (D) (p=0,q=1); (p=1,q=0); (p=1/3,q=2/3)
Game theory and strategic behaviour has come up 61 times in 6 exams since 2008.
What this question tests
This question is on Mixed-strategy Nash equilibrium, part of Game theory and strategic behaviour in Game Theory.
Equilibria where players randomise, found by making the opponent indifferent.
TestStop has 5 past-paper questions on this subtopic.
