Show whether the following statements are true or false.

i. If a game has a unique Nash equilibrium, then it is a dominant strategy equilib- rium as well.

ii. Consider a22(two players where each player has two strategies) normal form game. If a dominant strategy for player 1 is added, thenthe payoff to player 1atanyequilibrium of the new game must be at least as great as any Nash equilibrium payoff of player 1 in the original game.