\fQuestion 2: Game Theory [10 marks; 3,4,3] There are two petrol stations in Kingsford, Ampol and BP, which sell petrol at one of the three prices: 1) High (H): $1.80 a litre; 2) Medium (M): $1.40 a litre, and 3) Low(L): $1.00 There are 100 residents in Kingsford. Each resident buys 10 litres of petrol each week at one of the two stations. If prices between two stores differ by more than 50 cents per litre, all 100 residents buy petrol from the cheaper petrol station. Otherwise, o if two prices are equal, or o the two prices differ by less than 50 cents per litre, half of them buy at Caltex and the other half at BP. BP's profit = price set by BP X number of residents buying from BP X 10 Caltex's profit = price set by Caltex X number of residents buying from Caltex X 10(d) [3 marks] Consider a dynamic game where BP moves first, and Caltex moves second. That is, BP sets its price first following which Caltex sets its price. (i) (1 mark) Draw the extensive form game tree. Remember to clearly identify the nodes, specify player at each node, and write down the payoffs at terminal nodes. [Note: No further explanation needed for this part] (ii) (2 marks) Find the strategy played by each player in the unique subgame perfect Nash equilibrium of the extensive form game. For each subgame, briefly explain how you arrived at the best response for the corresponding player