2. Three drivers are racing towards a narrow tunnel which is only wide enough for two cars at a time. Each driver faces a choice to go straight (G'S) or to swerve (S). If they all play G'S, they will suffer serious injury and get payoffs equal to -8. If at least one driver swerves, the payoff to the driver(s) that swerved is 0 whereas the payoff to those that went straight is 1. The game is illustrated in the following table: Driver 3 -8-8,-8 1,0,1|1,1,0 1,0,0 01,1 0,0,1[01,0 0,0,0 (a) Identify all pure-strategy Nash equilibria. (3 marks) (b) Identify all Pareto efficient outcomes of the game. (3 marks) (c) Is there a mixed strategy Nash equilibrium of the game and what is the payoff to each player in this equilibrium? (6 marks) (d) Consider the following mechanism. An 'umpire' uses a randomisation device to select one cell in the game matrix with the probabilities shown in the following table: Driver 3 Driver 1, Driver 2 Show that this mechanism can be supported in a correlated equilibrium, and compute each driver's payoff. (6 marks)