4. Nash Equilibrium

Existence And Multiplicity — Quiz

Test your understanding of existence and multiplicity with 5 practice questions.

Practice Questions

Question 1

A strategy profile is a pure-strategy Nash equilibrium if:

Question 2

Consider this game. If Row chooses $A$ and Column chooses $X$, payoffs are $(3,3)$; if Row chooses $A$ and Column chooses $Y$, payoffs are $(0,2)$; if Row chooses $B$ and Column chooses $X$, payoffs are $(2,0)$; and if Row chooses $B$ and Column chooses $Y$, payoffs are $(1,1)$. How many pure-strategy Nash equilibria does this game have?

Question 3

Consider matching pennies. If Row chooses $H$ and Column chooses $H$, payoffs are $(1,-1)$; if Row chooses $H$ and Column chooses $T$, payoffs are $(-1,1)$; if Row chooses $T$ and Column chooses $H$, payoffs are $(-1,1)$; and if Row chooses $T$ and Column chooses $T$, payoffs are $(1,-1)$. How many pure-strategy Nash equilibria does this game have?

Question 4

When a game has more than one pure-strategy Nash equilibrium, this is called:

Question 5

Which statement best describes a game with no pure-strategy Nash equilibrium?