Answer one of the following.
(a) Question 3 (30% of marks).
Two athletes (1 and 2) compete annually and, prior to each contest, simultaneously choose whether to dope (D) or not
dope (ND). Each year, the contest winner gets a prize of 4200, while the loser gets nothing. The win probability of athlete
1, expressed in decimal form, in each possible case is:
Neither athlete dopes (ND,ND)
Only Athlete 1 dopes (D,ND)
Only Athlete 2 dopes (ND,D)
Both athletes dope (D,D)
p
0.9
0.5
p
where 0.5 < p < 1. An athlete whose cheating is detected incurs a penalty of 3000, where the probability of detecting doping,
again expressed in decimal form, is r and 0 < r < 1. Assume that the prize and penalty have the same real value over time, i.e.
no discounting.
(i) With the aid of a payoff matrix, determine the conditions for which both athletes doping and neither athlete doping,
respectively, is a Nash equilibrium outcome.
(ii) Prior to next year's contest, the World Anti-Doping Agency (WADA) can improve its testing capability so that the
probability of detecting cheating will increase from its current level of 0.4 to 0.5. How will this affect the doping
decision of the players if player 1 has a 75% win probability when neither and both dope? Explain any change.
