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 neither take the drug they tie and split the prize. Both athletes know that the drug imposes a health risk of X dollars, meaning there are future health costs. Draw the 2 x 2 payoff matrix describing the decisions the athletes face. For what X (cost of health risks) is taking the drug the Nash Equilibrium? Explain in writing. Does making the drug safer thus lowering the costs of the risks (X) make the athletes better or worse off? Explain your answer in writing.
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