Please help with 2.F

Mixed Strategies and Athletes on Steroids. Suppose two athletes are competing in an important race and either NO athlete has a choice of whether they should take performance enhancing steroids or not. Although there is a risk of getting caught, if one takes the drug the other doesn't, the one who does is likely to win and the payoff to winning is enough to offset the expected cost of getting caught. If both take the drug, neither athlete gets the edge and both face the chance of getting caught and punished, in which case, both are better off if neither took the drug. The game is given below. Horst q 1-q Steroids 1/2 No Drugs Jonathan 1/3 p Steroids (0, 0) (6, 2) 1- p No Drugs (1, 4) (3, 3) 1/3 1/2 1 P (2.A) What is the mixed strategy for Jonathan? Note that p = the probability that the Jonathan will take steroids and 1 - p is the probability that he will not. Show your work to get full credit. Hint: to find p*, Horst has to be indifferent between choosing taking steroids and not taking them. (4 points) (2.B)What is the mixed strategy for Horst? What is the percentage (q) of the time that he will randomly take steroids to enhance his performance? What is the probability (1 -q) that he will not? Show your work. Find q* that makes Jonathan indifferent between taking steroids and not taking them. (4 points) (2.F) In the graph below depict the best-response functions for Jonathan and Horst. That is, for Jonathan, what are the best choices of p for given levels of q? Label this curve BRlos, A similar analogy holds with respect to Horst and BRHout. Make sure you also depict the Nash Equilibria of this game, whether in pure or mixed strategies. (7 points)