Suppose that two cyclists are training to race each other. Each cyclist is considering whether to take steroids to improve their chance of winning the race. Assume that the cycling association does not currently have a policy against steroid use. If both cyclists take steroids, neither has an advantage and the payoffs (net of health costs) are $2 million per cyclist. If both cyclists don't take steroids, the payoffs are $3 million per cyclist. If one cyclist takes steroids and the other doesn't, the cyclist taking steroids receives a payoff of $5 million (net of health costs) and the other cyclist receives a $1 million payoff. a. Represent the game in a payoff matrix. b. What is the Nash equilibrium of the game? c. Would the cyclists be better off if the cycling association banned steroids and tested each cyclist for steroids prior to the race? Briefly explain.