Frank and Nancy met at a sorority party. They agreed to meet for a date at a local bar the next week.

Frank and Nancy met at a sorority party. They agreed to meet for a date at a local bar
the next week.
Regrettably, they were so fraught with passion that they forgot to agree on which bar
would be the site of their rendezvous.
Luckily, the town has only two bars, Rizotti’s and the Oasis. Having discussed their
tastes in bars at the party, both are aware that Frank prefers Rizotti’s to the Oasis and
Nancy prefer the Oasis to Rizotti’s.
The payoffs are as follows.
If both go to the Oasis, Nancy’s payoff is 3 and Frank’s payoff is 2.
If both go to Rizotti’s, Frank’s payoff is 3 and Nancy’s payoff is 2.
If they don’t both go to the same bar, each has a payoff of 0.
a. This game has no Nash equilibrium in pure strategies.
b. This game has a dominant strategy equilibrium.
c. There are two Nash equilibrium in pure strategies and a Nash equilibrium in
mixed strategies where the probability that Frank and Nancy go to the same bar
is 12 25 .
d. This game has two Nash equilibria in pure strategies and a Nash equilibrium in
mixed strategies where each person has a probability of 1 2 of going to each
bar.
e. This game has exactly one Nash equilibrium