Question

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

Required:
a. Draw a $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.

Answer 1

a) attached below.

b) for $x < $5000 will cause taking the drug to be part of the Nash equilibrium

c) will make the athletes feel better because the value their payoff will increase

Step-by-step explanation:

a) 2 * 2 payoff matrix describing the decision faced by the athletes

attached below

when both players take the drug the payoff for each player = $5000 - x

when neither player takes the drug the payoff for each player = $5000

When only one player takes the drug his payoff = $10000 - x

b) If we consider the value of $x to be involved in the Nash equilibrium then

; $5000 - $x > 0 becomes the best response

hence for $x < $5000 will cause taking the drug to be part of the Nash equilibrium

c) Lowering the negative effect of the drug ( i.e. when the value of x is reduced )

will make the athletes feel better because the value their payoff will increase