7. Two cyclists of equal ability are competing in the Tour de Chance for a prize of $10,000. A banned substance is available. If one athlete takes the substance and the other does not, the one who takes it wins the prize. If both or neither takes the substance, they tie and split the prize. Taking the substance, however, imposes health risks as well as the possibility of testing positive and being banned from the sport for life. Assume these costs can be quantified and have a combined value of X dollars.

Set up the 2 X 2 payoff matrix for this game.

i. If X equals $2500 , the Nash equilibrium for this game would be:

a. Both players take the banned substance. b. Neither player takes the banned substance. c. One player takes the banned substance, and the other does not. d. No Nash equilibrium exists in this game if X = $2500.

ii. If X equals $7500 , the Nash equilibrium for this game would be:

a. Both players take the banned substance. b. Neither player takes the banned substance. c. One player takes the banned substance, and the other does not. d. No Nash equilibrium exists in this game if X = $7500.

Now suppose that the two cyclists have different levels of risk aversion and thus do NOT have the same value of X in this case. Assume that Player 1 has an X value (X1) of $2500 , while Player 2 has an X value (X2) of $7500.

Set up the payoff matrix in this case.

iii. With these values of X1 and X2 , the Nash equilibrium for this game would be:

a. Player 1 takes the banned substance, while Player 2 does not.

b. Player 2 takes the banned substance, while Player 1 does not.

c. Both Player 1 and Player 2 take the banned substance.

d. No Nash equilibrium exists in this game with the values of X1 and X2 in this case.

iv. Which of the following observations might be consistent with your findings in this question:

a. An inverse correlation between the number of players banned for PED use in Major League Baseball and the GDP / capita of their country of origin.

b. An inverse correlation between athletes banned for PED use and equity in the distribution of prize money for tournaments in their sports.

c. Both (a) and (b) are true.

d. Neither (a) nor (b) is true.

Thank you