Answer
a) Please see the decision box.
b) $X \leq5000$ for both athletes to take the drug.
c) Making the drug safer makes athletes more likely to take the drug.
Work Step by Step
b) If Athlete B takes the drug, Athlete A should take the drug as long as $X \leq5000$. If Athlete B doesn't take the drug, Athlete A should take the drug as long as $X \leq5000$. (In the second case, if neither athlete takes the drug, Athlete A gets 5,000 dollars. However, if Athlete A takes the drug while Athlete B doesn't, Athlete A nets $10000-X$.)
If Athlete A takes the drug, Athlete B should take the drug as long as $X \leq5000$. If Athlete A doesn't take the drug, Athlete A should take the drug as long as $X \leq5000$. (In the second case, if neither athlete takes the drug, Athlete B gets 5,000 dollars. However, if Athlete B takes the drug while Athlete A doesn't, Athlete B nets $10000-X$.)
Thus, as long as $X \leq5000$, both athletes would take the drug.
c) If we lowered $x$ to $3000$, both athletes would take the drug. As long as $x$ is under $5000$, then the athletes would still take the drug.
