8) Chanchal and Chloe sell ice cream on 5th Avenue along Central Park. For each ice cream they sell, they get a profit of $0.50. Each morning they must decide at which of the three legally permitted locations they should sell their ice cream-at 110th Street and 5th Avenue, at 90th Street and 5th Avenue and at 70th Street and 5th Avenue. In each of the three locations, there are 180 customers per day, and each customer buys one unit of ice cream from the nearest vendor. If they set up at the same location then they get half of the customers. For example, if Chanchal and Chloe both choose 90th Street then half of customers from all three locations will buy from Chanchal and the other half will buy from Chloe, so that each gets a profit of $135. If Chanchal is at 110th Street and Chloe is at 90th Street then Chanchal will get everyone at 110th Street, and Chloe will get all the customers from both the 90th Street and 70th Street locations. If Chanchal is at 70th Street and Chloe is at 110th Street, then they will each get their respective customers plus half the customers from the 90th Street location. a) Draw out the strategies and payoffs for Chanchal and Chloe in a matrix. b) Is Chanchal choosing 110th Street and Chloe choosing 70th Street a Nash equilibrium? Why? c) Is Chanchal choosing 90th Street and Chloe choosing 110th Street a Nash equilibrium? Why? d) What choices, if any, are Nash equilibria for this game? 8) Chanchal and Chloe sell ice cream on 5th Avenue along Central Park. For each ice cream they sell, they get a profit of $0.50. Each morning they must decide at which of the three legally permitted locations they should sell their ice cream-at 110th Street and 5th Avenue, at 90th Street and 5th Avenue and at 70th Street and 5th Avenue. In each of the three locations, there are 180 customers per day, and each customer buys one unit of ice cream from the nearest vendor. If they set up at the same location then they get half of the customers. For example, if Chanchal and Chloe both choose 90th Street then half of customers from all three locations will buy from Chanchal and the other half will buy from Chloe, so that each gets a profit of $135. If Chanchal is at 110th Street and Chloe is at 90th Street then Chanchal will get everyone at 110th Street, and Chloe will get all the customers from both the 90th Street and 70th Street locations. If Chanchal is at 70th Street and Chloe is at 110th Street, then they will each get their respective customers plus half the customers from the 90th Street location. a) Draw out the strategies and payoffs for Chanchal and Chloe in a matrix. b) Is Chanchal choosing 110th Street and Chloe choosing 70th Street a Nash equilibrium? Why? c) Is Chanchal choosing 90th Street and Chloe choosing 110th Street a Nash equilibrium? Why? d) What choices, if any, are Nash equilibria for this game