A and B are runners competing for a gold medal in the 100 meter dash. Both can take steroids to enhance their speed. Let cc and y denote quantities of steroids used by A and B. If at least one of x and y is non a? zero, the probability that A wins the race is m and the probability that B wins the race is 3%,. If neither party takes any steroids each wins the race with probability 1/2. The value of winning the race is 100 and the cost, inclusive of the adverse effects on the runner's own health, is 1 per unit of steroids consumed. Thus A's objective function is if??? a: and B's objective function is g3 y. a) If A and B make their choice regarding steroids simultaneously, what is the Nash Equilibrium values of a: and y for this game? b) Is the equilibrium efcient? If not, state an outcome that Pareto dominates it. c) Explain the nature of the externality problem in this scenario. d) Would these runners embrace an institution that limited their ability to use steroids