Answer to Question 1
The statement is false. If one player has a dominant strategy and the other player knows it, then the outcome is predictable. For example, if player A will go right when player B moves left and vice versa, we can predict what player A will do if player B has a dominant strategy. If player B's dominant strategy is to move right, then we know that player A will move left.
Answer to Question 2
The principle of second best rests on the fact that just because a tax distorts an economic decision does not always imply that such a tax imposes an excess burden. If previously existing distortions exist, such a tax may actually improve efficiency.
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