4. Nash Equilibrium
Pure-strategy Equilibria — Quiz
Test your understanding of pure-strategy equilibria with 5 practice questions.
Practice Questions
Question 1
Consider the game below, where the first payoff in each cell is for Player 1 and the second payoff is for Player 2:
Player 2: $C$ $D$
Player 1 $C$ $(3,3)$ $(0,5)$
Player 1 $D$ $(5,0)$ $(1,1)$
Which strategy profile is a pure-strategy Nash equilibrium?
Player 2: $C$ $D$
Player 1 $C$ $(3,3)$ $(0,5)$
Player 1 $D$ $(5,0)$ $(1,1)$
Which strategy profile is a pure-strategy Nash equilibrium?
Question 2
The game below is matching pennies:
Player 2: $H$ $T$
Player 1 $H$ $(1,-1)$ $(-1,1)$
Player 1 $T$ $(-1,1)$ $(1,-1)$
How many pure-strategy Nash equilibria does this game have?
Player 2: $H$ $T$
Player 1 $H$ $(1,-1)$ $(-1,1)$
Player 1 $T$ $(-1,1)$ $(1,-1)$
How many pure-strategy Nash equilibria does this game have?
Question 3
Consider the game below:
Player 2: $L$ $R$
Player 1 $U$ $(2,4)$ $(1,0)$
Player 1 $D$ $(3,1)$ $(0,2)$
If Player 1 plays $U$, what is Player 2's best response?
Player 2: $L$ $R$
Player 1 $U$ $(2,4)$ $(1,0)$
Player 1 $D$ $(3,1)$ $(0,2)$
If Player 1 plays $U$, what is Player 2's best response?
Question 4
Consider the game below:
Player 2: $A$ $B$
Player 1 $X$ $(4,1)$ $(3,0)$
Player 1 $Y$ $(2,2)$ $(1,1)$
Which profile is a pure-strategy Nash equilibrium?
Player 2: $A$ $B$
Player 1 $X$ $(4,1)$ $(3,0)$
Player 1 $Y$ $(2,2)$ $(1,1)$
Which profile is a pure-strategy Nash equilibrium?
Question 5
Consider the game below:
Player 2: $L$ $R$
Player 1 $Top$ $(3,0)$ $(0,4)$
Player 1 $Middle$ $(1,1)$ $(4,5)$
Player 1 $Bottom$ $(2,2)$ $(1,0)$
Which profile is a pure-strategy Nash equilibrium?
Player 2: $L$ $R$
Player 1 $Top$ $(3,0)$ $(0,4)$
Player 1 $Middle$ $(1,1)$ $(4,5)$
Player 1 $Bottom$ $(2,2)$ $(1,0)$
Which profile is a pure-strategy Nash equilibrium?