Question 4 2 pts Just like any other undergraduate student, Afshan knows the importance of arriving before her roommate when it comes to moving into her dorm room. However, she also recognizes the difculty in moving at exactly the same time as her roommate; everyone is cramped in the stairways. hallways, and in the elevator, and there's a limit to the number of bodies that can fit in that small room at once to unpack. Since Afshan is a rst-year student, the university assigned Roopali to be her roommate. Assume that it is impossible for either roommate to get in touch with the other one prior to move-in day. So each roommate must decide simultaneously whether to arrive in the morning or afternoon. If they move in at the same time, each receives a payoff of 0; if they move in at different times, each receives a positive payoff, but the person arriving in the morning is better off. The following payoff matrix represents the game they must play. Roopali Morning Afternoon Morning Afternoon What are the pure strategy Nash equilibria? [salad] V Let's take a look at mixed strategies. Suppose 3:: {1 at} is the probability that Afshan plays Morning {Afternoon} and y {1 y} is the probability that Roopali plays Morning {Afternoon}. At a certain value of 'y, Afshan is indifferent to choosing between always selecting the morning and always selecting the afternoon. What is this value of y? [59'3\"] V At a certain value of :8, Roopali is indifferent to choosing between always selecting the morning and always selecting the afternoon. What is this value of :8? [59'3\"] V Given your solution to the game above, choose the plot which shows the best response functions of both students. (3?: Afshan's probability of choosing morning, '9: Roopali's probability of choosing morning) 10 10 0.9 0.9 0.8 07 0.7 0.6 0.6 (a) x 0.5 * 0.5 0.4 0.4 0.3 0.2 0.3 0.1 0.2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 (d) 10 1.0 0.9 0.9 0.8 0.8 07 07 0.6 0.6 (c) * 0.5 * 0.5 0.4 0.4 0.3 0.2 0.3 0.1 0.2 0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0