1. Arif and Aisha agree to meet for a date at a local dance club next week. In their enthusiasm, they forget to agree which venue will be the site of their meeting. Luckily the town has only two dancing venues, Palms and Oasis. Having discussed their tastes in dancing venues last week, both know that Arif prefers Palms to the Oasis and Aisha prefers the Oasis to Palms. In fact, their payoffs reflect that if both go to Oasis, Aisha's utility is 3 and Arif's 2, while if both go to Palms Arif's utility is 3 and Aisha's is 2. If they do not go to the same venue, then they both have a utility of 0.

(a) Write the payoff matrix and explain whether there are any pure Nash equilibria. Carefully explain what these are and why. Comment on the existence of any dominant strategy equilibria.

(b) Please calculate mixed strategy equilibria, if any, and then derive the probability that Arif and Aisha will find themselves at the same venue. Carefully explain the steps to your solution; a numerical answer with explanation

(c) What if on the day of the date, Arif leaves earlier for the venue and then calls Aisha to tell her where he is? Is there a first mover advantage and what form does it take? Carefully explain your answers by drawing the game in a sequential form and explain what the equilibrium will be.