Frank and Nancy Met at a Sorority Sock Hop

Frank and Nancy met at a sorority sock hop.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 sock hop, both are aware that Frank prefers Rizotti's to the Oasis and Nancy prefer the Oasis to Rizotti's.In fact, the payoffs are as follows.If both go to the Oasis, Nancy's utility is 3 and Frank's utility is 2.If both go to Rizotti's, Frank's utility is 3 and Nancy's utility is 2.If they don't both go to the same bar, both have a utility 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.