Self Test

Dominance, Best Replies, and Equilibria

These problems test your conceptual understanding of best replies, 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 also be weakly dominated.

	True
	False

Question 4.

If strategies A and X are strictly dominant strategies, then strategy profile {A,X} must be the only equilibrium of the game.

	True
	False

Question 5.

If {A,X} is the only equilibrium of the game, then A and X must be dominant strategies.

	True
	False

Question 6.

If {B,Y} is an equilibrium of the game, then strategy B cannot be strictly dominated.

	True
	False

Question 7.

If {B,Y} is an equilibrium of the game, then strategy B cannot be weakly dominated.

	True
	False

Question 8.

If strategy A is strictly dominant, then it must be a best reply to strategy 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 strictly dominant strategy.

	True
	False