Two bike riders, Floyd and Lance, are scheduled to race. Each wants to maximize his chance of winning the race; neither has any reservations about taking steroids if that will help win the race. The payoffs are as follows:
If neither takes steroids, each has a 50 percent chance of winning the race.
If Floyd takes steroids and Lance does not, Floyd has a 70 percent chance of winning the race.
If Lance takes steroids and Floyd does not, Lance has an 80 percent chance of winning the race.
If both take steroids, each has a 50 percent chance of winning the race.
a) Draw a “payoff matrix” illustrating this game
b) What is the Nash equilibrium outcome of this game? Explain
c) Suppose the two racers agreed in advance not to take steroids, in order to preserve their health. Would the agreement be credible? Explain your answer