\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{b} [II marks] State whether 1he following statements are True er False and explain yeur answer. {i} Sis-remain! 1: There exists a Nash equilibrium where BF cheeses M and Carter: cheeses L. [1 mark] {ii} Statement 2: There exists a Nash equilibrium where BF cheeses L and Calla: cheese H. [1 mark]