In a household with n people, there is a common sink that is filled with dirty dishes. Only 1 member of the household has to do the dishes. Each member obtains v units of utility if someone(anyone) does the dishes. The person that does the dishes pay a personal cost of c. That is, if person i does the dishes, then he obtains the payoff v — c; if person i does not do the dishes but at least one other person does, then person i gets v; finally, if none of the n members do the dishes, then person i obtains zero. Assume v >c Find the symmetric MNE of this game (let p be the probability that the person DOES NOT do the dishes).
a) p= (v/c)ni
b) p= (c/v) n=1
c) p= (c/v)-1
d) p= (v/c)1=n