Determine whether each of the following statements is true or false:

(1) In a Nash equilibrium of a strategic game, each player must best respond to her opponents' actions, therefore, no other action profile can be unanimously preferred by all the players to a Nash equilibrium.

(2) (Recall that a strategic game is called Dominance Solvable if and only if exactly one action profile remains after iteratively eliminating all strictly dominated actions.) If a strategic game is dominance solvable, it can have at most one Nash equilibrium.

(3) Consider the baseline Hotelling-Downs model introduced in class. The Nash equilibria of the game will remain unchanged if, instead of maximizing their probabilities of winning the election, each party / candidate seeks to maximize their vote share.