Two athletes of equal ability are competing for a prize of $10,000. Each is deciding whether to take a dangerous performance-enhancing drug. If one athlete takes the drug, and the other does not, the one who takes the drug wins the prize. If both or neither take the drug, they tie and split the prize. Taking the drug imposes health risks that are equivalent to a loss of X dollars.
a. Draw a 2×2 payoff matrix describing the decisions the athletes face.
b. For what X is taking the drug the Nash equilibrium?
c. Does making the drug safer (that is, lowering X) make the athletes better or worse off? Explain.