Which is true for the following game?1 \2 L C RT 3, 5 4, 6 5, 9M 6, 4 4, 6 8, 4B 4, 6 6, 4 3, 5(A) (T,R) is a Nash equilibrium(B) There is a Nash equilibrium in which Player 1 plays M and B with equal probability andPlayer 2 plays each action L, C and R with positive probability(C) There is a Nash equilibrium in which Player 1 plays each action T, M and B with positiveprobability and Player 2 plays each action L, C and R with positive probability(D) There is a Nash equilibrium in which Player 1 plays M and B with equal probability andPlayer 2 plays L and C with equal probability
Question
Which is true for the following game?1 \2 L C RT 3, 5 4, 6 5, 9M 6, 4 4, 6 8, 4B 4, 6 6, 4 3, 5(A) (T,R) is a Nash equilibrium(B) There is a Nash equilibrium in which Player 1 plays M and B with equal probability andPlayer 2 plays each action L, C and R with positive probability(C) There is a Nash equilibrium in which Player 1 plays each action T, M and B with positiveprobability and Player 2 plays each action L, C and R with positive probability(D) There is a Nash equilibrium in which Player 1 plays M and B with equal probability andPlayer 2 plays L and C with equal probability
Solution
To answer this question, we need to understand what a Nash equilibrium is. A Nash equilibrium is a concept of game theory where the optimal outcome of a game is one where no player has an incentive to deviate from his chosen strategy after considering an opponent's choice.
Let's analyze each option:
(A) (T,R) is a Nash equilibrium To check this, we look at the payoff for each player at (T,R). Player 1 gets 2 and Player 2 gets 5. If Player 1 deviates and plays M, he gets 6 which is better for him. So, (T,R) is not a Nash equilibrium.
(B) There is a Nash equilibrium in which Player 1 plays M and B with equal probability and Player 2 plays each action L, C and R with positive probability For this to be true, Player 1 should be indifferent between M and B given Player 2's strategy and Player 2 should be indifferent between L, C and R given Player 1's strategy. This is not possible as the payoffs for different actions are not the same.
(C) There is a Nash equilibrium in which Player 1 plays each action T, M and B with positive probability and Player 2 plays each action L, C and R with positive probability This is also not possible as the payoffs for different actions are not the same.
(D) There is a Nash equilibrium in which Player 1 plays M and B with equal probability and Player 2 plays L and C with equal probability For this to be true, Player 1 should be indifferent between M and B given Player 2's strategy and Player 2 should be indifferent between L and C given Player 1's strategy. This is not possible as the payoffs for different actions are not the same.
So, none of the options are true for the given game.
Similar Questions
Which is true for the following game?1 \2 L C RT 2, 3 3, 4 4, 8M 5, 6 4, 3 7, 1B 6, 2 5, 5 2, 4(A) There is a mixed strategy Nash equilibrium in which Player 1 plays both M and B withpositive probability and Player 2 plays both L and C with positive probability(B) The best response of Player 2 to M is C(C) (B,C) is the only Nash equilibrium(D) (M,L) is a Nash equilibrium
Which is false for the following game?1 \2 L C RT 3, 2 0, 3 3, 3M 5, 0 4, 1 3, 1B 2, 2 4, 5 1, 1(A) (M,C) and (B,C) are the only pure strategy Nash Equilibria(B) There is a Nash equilibrium in which R is played with positive probability(C) There is no Nash equilibrium in which L is played with positive probability(D) There is no Nash equilibrium in which both players choose two of their actions with positiveprobability
Consider the following game in which Sally can play T or B and John chooses between L or R. Each player makes their choice simultaneously. If Sally chooses T and John chooses L, Sally gets a payoff of 3 and John has a payoff of 7. If Sally plays T and John R, Sally’s payoff is 5 and John gets 1. If Sally Chooses B and John L, the payoffs are 1 to Sally and 2 to John. Finally, if Sally chooses B and John R, the payoffs are 4 to Sally and 3 to John. What are the Nash equilibria of the game?Group of answer choices(T,L) and (B,R)(T,L)(B,R)None of the other answers are correct.(T, R)
In a Nash equilibrium
This table shows a game played between two players, A and B. The payoffs are given in the table as (Payoff to A, Payoff to B). B LeftCenterRight Up(8, 4)(4, 10)(6, 6)AMiddle(6, 2)(10, 6)(10, 4) Down(2, 6)(8, 8)(12, 2)Refer to Table 17-16. Which of the following outcomes represents a Nash equilibrium in the game?Group of answer choicesMiddle-CenterDown-CenterUp-LeftMore than one of the above is a Nash equilibrium in this game.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.