Two stars - the 100-meter gold medallist and the 200-meter gold medallist - agree to a 150- meter duel. Before the race, each athlete decides whether to improve his performance by taking anabolic steroids. If one athlete takes steroids and the other doesn't, the first athlete will win (but not in an honest way). If both athletes take the steroids, then it will be a tie. Each athlete's utility payoff is 60 from winning the race, 30 from tying, and 0 from losing. Each athlete's utility of taking steroids is -18.

a) Model the scenario as a game in which the players simultaneously decide whether to take steroids.

b) What is the Nash equilibrium? Is the game a prisoner's dilemma? Explain

c) Suppose that the 200-meter athlete's utility from taking steroid is -36, while the other's remains -18. What is the Nash equilibrium? Is the game prisoner's dilemma?