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.

The best option is when both athletes decide not to take drugs and each earns $5,000.

Explanation:

In a Nash equilibrium scenario:

                                                 Athlete 1's decision

                                      take drug                   do not take drug

Athlete 2's                     $5000 - x/                        $0 /

decision                                  $5,000 - x                     $10,000 - x

take drug

do not                           $10,000 - x/                        $5,000 /  

take drug                                          $0                               $5,000

The best possible situation occurs when both athletes decide not to take the drugs. In this situation both athletes win $5,000. If both athletes decide to take the drug and charge the price, they will both earn $5,000 - X.

The Nash equilibrium should show the situation where both players win the most regarding the other player's strategy.

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