a l 5. Two swimmers players 1 and 2 are to participate in a runoff. Each player has the option of using a performance-enhancing steroids (s) 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: S 1'1 am 1,1 11 1,1 0,0 (a) Analyze this game and explain why an anti-doping policy is needed. [10pts] (1)) Suppose the international Olympics organization (IOC, player 3) intervene. Let us further assume that 100 can only test one swimmer. IOC has two actions: testing player 1 (t1) and testing player 2 (t2). The doping player who is caught by ICC 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. S D S II S 1b,1,1 1b,1,1 s 1,1b,1_ n n 1.45.1 1. Explain why it is not a Nash equilibrium for IOC to always test player 1. [10pts] 2. Solve for one Nash equilibrium of this game (you don't have to construct all Nash equilibria of this game). [10pts]