AGT - Homework week 1
A live, indoor concert is about to take place in Amsterdam. The number of people who has
purchased a ticket is n. However, a contagious virus is currently present. Experts suggested
that as long as the audience is up to n-1 people, they shouldn’t be worried about getting
infected by the virus. If more than n-1 people decide to go to the concert simultaneously, everyone will get infected, and each person prefers to go home instead. But if at least one person
who has a ticket does not go, the concert will have n-1 or fewer people, and nobody will get
infected. We will say that the concert is safe when the audience consists of n-1 people or less,
and unsafe when there are more than n-1 people (n in this case). Before the concert starts,
each person decides, simultaneously and independently, whether to go to the concert or stay
at home. Each individual prefers to be at home over being in an unsafe concert, but otherwise
prefers to be in a safe concert (with n-1 or less people including herself). All people maximize
their expected utility. Each one is indi↵erent between (i) staying at home, or (ii) being in an
unsafe concert with probability 18 and in a safe concert with probability 78 .
a. Describe the game formally (player set, actions etc.)
b. Describe the Nash equilibria where each person who has a ticket chooses a pure strategy.
c. For n = 4 find the mixed-strategies Nash equilibria where each person with a ticket goes to
the concert with the same probability p (i.e. determine the correct p).
d. For general n find the Nash equilibrium where each person with a ticket goes to the concert
with the same probability p.
e. One day before the concert, the experts changed their mind and suggested that if there
are more than n-3 people in the audience, everyone would get infected. For n = 4 find the
symmetric mixed-strategy Nash equilibrium where each person with a ticket goes to the concert
with the same probability p (i.e. determine the correct p).
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