6. Two swimmers players 1 and 2 are to participate in a runoff. Each player has the option of using a performance-enhancing steroids (8) or not using it (n). The two players are equally good. A player will win if he is the only one to use the drug. The payoff matrix is as follows: n 1 S n mm (a) Analyze this game and explain why an anti-doping policy is needed. [5pts] CD - a: (3 ul' (b) Suppose the international Olympics organization (IOC, player 3) intervene. Let us further assume that IOC can only test one swimmer. 100 has two actions: testing player 1 (t1) and testing player 2 (t2). The doping player who is caught by 100 will lose the game and pay a penalty of b > 0, and the 100 in this case will improve its image. The payoffs of the three-player game are as follows. 1. Explain why it is not a Nash equilibrium for 100 to always test player 1. [5ptS] 2. Solve for one Nash equilibrium of this game (you don't have to construct all Nash equilibria of this game). [5pts]