Chapter $18$ Problems & Applications

$8.$ Problems and Applications Q$8$

Two athletes of equal ability are competing for a prize of $$6,000.$ 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.

Complete the following payoff matrix describing the decisions the athletes face. Enter Player One's payoff on the left in each situation, Player Two's on the right.

Player Two's Decision

True or False: The Nash equilibrium is taking the drug if $x$ is greater than $$3,000.$

True

False

Suppose there was a way to make the drug safer $($that is$,$ have lower $x).$

Which of the following statements are true about the effects of making the drug safer? Check all that apply.

$$ It lowers the likelihood of taking the drug.