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
Question
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
Solution
The game matrix seems to be incomplete, which makes it difficult to accurately answer the question. However, based on the information provided, we can make some assumptions:
(A) We can't confirm or deny this without the complete game matrix. (B) We can't confirm or deny this without the complete game matrix. (C) This could be false if there is a Nash equilibrium where L is played with positive probability. However, without the complete game matrix, we can't confirm this. (D) This could be false if there is a Nash equilibrium where both players choose two of their actions with positive probability. However, without the complete game matrix, we can't confirm this.
In conclusion, without the complete game matrix, it's impossible to definitively answer this question.
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