Answer whether each of the following statements is True or False. Explain why.

(a) If we add 10 to Player 1's payoff in every cell of the matrix, the set of pure Nash equilibria is unchanged.

(b) If we add 10 to Player 1's payoff in every cell of the matrix, the set of mixed Nash equilibria is unchanged.

(c) If a game has a finite number of players and actions, there always exists a pure strategy Nash equilibrium.

(d) If two different actions are played (with positive probability) in a mixed strategy Nash equilibrium, then these actions give the same expected payoffs (given that the other players do not deviate from the equilibrium).

(e) If an action is not strictly dominated in a strategic game without randomization, it cannot be strictly dominated when randomization is allowed.