Each student in a class has the option to remain silent or ask the professor to cancel class. If any students asks to cancel class, all students get a payoff of $r$. However, the student that asks incurs a cost of $c < r$ so that his payoff if $r-c$. If none of the students ask, they all get a payoff of $0$.
If the students adopt pure strategies, what is the pure strategy Nash Equilibria for the game?
If all students adopt mixed strategies (i.e. student $i$ asks with probability $p_i$ for $i = 1,...,n$), is there a mixed strategy Nash Equilibria for the game?
I would appreciate if someone could briefly explain each part. I'm not sure how to deal with the case of arbitrary $n$. Every example of NE I've seen has a table with underlined values, and choosing the one with all values underlined represents a Nash Equilibria.