The 100-meter Olympic gold medalist and the 200- meter Olympic gold medalist have agreed to a 150- meter duel. Before the race, each athlete decides whether to improve his performance by taking anabolic steroids. Each athlete's payoff is 20 from winning the race, 10 from tying, and 0 from losing. Furthermore, each athlete's utility of taking steroids is -6. Model this scenario as a game in which the players simultaneously decide whether to take steroids.
a. What is the Nash equilibrium? Is the game a prisoners' dilemma? Explain.
b. Suppose that one athlete's utility of taking steroids is -12, while the other's remains at -6. What is the Nash equilibrium? Is the game a prisoners' dilemma?