2. After running an unsuccessful Marathon, Phil was discharged with great dishonour

from Athens' army. He later became the happy manager a rather successful convenience

store near the city's main square2. Unfortunately, after a few years of relative stability, a

plague erupts in Athens and lockdown is declared by local authorities. Phil reads on the

news-scroll than panic is spreading in the city as people begun to hoard toilet paper from

local shops. On the bottom of the news-scroll, he also reads the following sentence from an

interview to the famous pollster Pythagoras:

"We are living in obscure times [:::] It appears that each Athenian person I interviewed is

trying to stash 1.1 meters of toilet paper times the average of the amount stashed by her

fellow citizens!.

Phil has to decide how much toilet paper he should put on sale on display. He can choose

any quantity between 0 and 100 meters. Indeed, as toilet paper rolls on shelf look bad and

take space for more luxury merchandise, he wants to be as precise as possible. To make such

choice, he has to predict the average demand for toilet paper from his own customers.

(a) If Phil assumes his customers are fully rational, what are the Nash equilibria of this

game as measured in terms of average customer's demand for toilet paper?

(b) Assume instead that Phil knows that out of his local community made of N = 20

customers, only 19 are rational. In addition to these, there is also an old stubborn chap,

called Plato, that bought 3m of toilet paper no matter what, since Phil opened the shop,

and he's not going to change his habits. Compute the average customer's demand for

toilet paper.