Self Test

Dominant Strategies & Best Replies

These problems test your understanding of best responses, dominant and dominated strategies, and equilibria. They are not easy, and you may want to review the definitions of each of these concepts as you answer these questions.

For the following questions, consider a two-player game, with three strategies for each player. Payoffs are not given.

		Player 2
		X	Y	Z
Player 1	A
	B
	C

Question 1.

If strategy Y is strictly dominant, then strategies X and Z must be strictly dominated.

	True
	False

Question 2.

If X is a strictly dominated strategy, then either Y or Z must be a dominant strategy.

	True
	False

Question 3.

If a strategy is strictly dominated, then that strategy must be weakly dominated.

	True
	False

Question 4.

If the strategies A and X are strictly dominant strategies, then (A,X) must be the only equilibrium of the game.

	True
	False

Question 5.

If (A,X) is the only equilibrium of the above game, then A and X must be dominant strategies.

	True
	False

Question 6.

If (B,Y) is an equilibrium of the above game, then B cannot be strictly dominated.

	True
	False

Question 7.

If (B,Y) is an equilibrium of the above game, then B cannot be weakly dominated.

	True
	False

Question 8.

If the strategy A is strictly dominant, then it must be a best response to Z.

	True
	False

Question 9.

If strategy A strictly dominates strategy B, then A must be a strictly dominant strategy.

	True
	False

Question 10.

Each player can have at most one dominant strategy.

	True
	False