2-player game

Consider the following 2-player game in which player 1 chooses between T and B, and player 2 chooses between L, C and R. The payoffs are presented in the table below.

(a) Is there a strictly dominated strategy for any player? If so, identify it.

(b) Is the strategy profile ((1/2,1/2), (1/4,1/2, 1/4)), a Nash equilibrium, or not? Briefly explain with reference to your answer to Part (a) of this question.

(c) State if there exists a pure strategy Nash equilibrium in this game. No justification is required.

(d)  Solve for the unique (completely) mixed strategy Nash equilibrium of the game. Show your calculations. (There is no need to prove uniqueness.)

(e)  Consider a new game in which the payoff to Player 2 in the outcome (T,C) is increased, while all other payoffs remain unchanged. The new game also possesses only one Nash equilibrium, in which both players put strictly positive probabilities on at least two of their actions. In the Nash equilibrium of the new game, will Player 2 play C more frequently than in the Nash equilibrium of the original game? Briefly explain your answer.

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