2. Fixed costs You are a smuggler who owns a ship and you have some goods that you plan to smuggle via ship. If you can reach your destination, you can sell the goods on the ship for a net profit of V. In order to reach your destination, you must pass two points, unimaginatively known as point 1 and point 2. Located at each point is a corrupt police officer who will want a bribe. If and when you reach point i = 1, 2, police officer i will find you, and he will make a take-it-or-leave-it demand, Pi. If you accept the demand, then you pay the police officer Pi, and can continue your journey; if not, you return home and have a net return of 0. So to be clear, if you never turn back then you journey looks as follows: Home - point 1 - point 2 - destination Each corrupt police officer tries to maximise the amount he earns. You try to maximise profits (money from goods minus payments to police officers). We assume that this game is one of perfect information. That is, you know with certainty that if you reach point i E {1, 2} that you will meet police office i. Everyone knows V, police officer 2 knows the demand of police officer 1. And so on. (a) 10 marks Draw the game tree. (b) 15 marks Compute the subgame-perfect equilibrium and its associated payoffs. (c) 5 marks Identify at least one Nash equilibrium that is not subgame perfect