This is a question of economic strategy analysis, I need to finish it within 30 minutes

A town has only two movie cinemas, cine1 and cinez. At the start of 2021 , both cinemas choose a price for their tickets for the whole year. Suppose that, if cine1 chooses a price p1 and cine2 chooses a price p2, then the total number of tickets sold by cine1 is equal to: Q1 = 600 60p1 + 30p2 and the total number of tickets sold by cine2 is equal to: q2 = 400 50p2 + 30p1 Each cinema wants to maximise its total profit, which is given by its total revenue minus its total cost. The marginal cost for each cinema is 0 (Le, each cinema only has xed costs). You may assume in all calculations below, without verifying, that all numbers of tickets sold are strictly positive. You can also take prices and numbers sold as being continuous and perfectly divisible; i.e., it is possible that a cinema sells g of a ticket, or even 3.14159265 tickets are sold, for instance. Write your payoff answers rounded to the nearest cent. (a) Suppose that the two cinemas choose their prices on January 1, 2021, simultaneously and independently. Model the situation as a game for the players cine1 and cine2 by specifying: a. the set of strategies for each of cine1 and cine2 b. the payoff function 1.11 for cine1 and the payoff function uz for cine2 (4 marks) (b) Using your answers in (a), determine the NE in this game, as well as the resulting payoffs for the cinemas. (6 marks) Now suppose that cine1 decides to choose its price on December 31, 2020, and then immediately makes this price known to cine2 and everyone else. Cine2 must then choose its price one day later, on January 1, 2021, knowing the price of cine1. (c) Analyse this new situation in terms of what the two cinemas will do, and what the resulting payoffs will be for each cinema. (4 marks) (d) If cine2 must choose its price on January 1, 2021, but cine1 can decide to choose (and make public) its price either on December 31, 2020 prior to cine2, or on January 1, 2021, simultaneously with and independently of cine2, then what will cine1 do? Is cine2 happier when cine1 can price a day earlier, compared to the case when both cinemas price simultaneously? (6 marks)