game tree, nash equilibrium, mixed strategy.

Suppose that two macho hoodlums from opposing street gangs are speeding straight toward each other on a quiet and narrow road. The driver that deviates (or swerves) would be labelled a coward, whereas the driver that stays on course would gain gang admiration. If neither of them swerve, they will crash into each other and die a horrible death. The (benet) pay-offs to this game are shown in the matrix below: .S'werves Gangster A Stays on course Gangster B Swerves Stays on course 20 , 20 10 , 30 30, 10 0, 0 a) Draw the extensive form (or game tree) for this game, based on the information given. b) Find the pure-strategy Nash equilibrium or equilibria. (3) Explain how you nd a mixed-strategy equilibrium. (2 marks) (2 marks) (4 marks)