Two boxers, Brutus and Floyd, are training to fight each other. Each boxer is considering whether to take steroids to improve his chance of winning the fight. Assume that the boxing association does not have a policy against steroid use. If both boxers take steroids, neither has an advantage and the payoffs (net of health costs) are $3 million per boxer. If both boxers don’t take steroids, the payoffs are $4 million per boxer. If one boxer takes steroids and the other doesn’t, the boxer taking the steroids receives a payoff of $6 million (net of health costs) and the other boxer receives a $1 million payoff.
a. Represent the preceding information in a normal-form game (payoff matrix).
b. What is the Nash equilibrium?
c. Would the boxers be better off if the boxing association banned steroids and tested each boxer for steroids prior to a fight? Explain.