5. Two swimmers players 1 and 2 are to participate in a runoff. Each player has the option of using a performance-enhancing steroids (5) 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 n 1,1m (a) Analyze this game and explain why an anti-doping policy is needed. [lOpts] (b) Suppose the international Olympics organization (IOC, player 3) intervene. Let us further assume that 100 can only test one swimmer. 100 has two actions: testing player 1 (t1) and testing player 2 (t2). The d0ping 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. S II S [l s 1b,1,1 1b,1,1 s 1,1b,1 1,1,0 n 1,1,0 0,0,0 'n 1,1b,1 0,0,0 t1 t2 1. Explain why it is not a Nash equilibrium for 100 to always test player 1. [10pts] 5:24. 2. Solve for one Nash equilibrium of this game (you don't have to construct all Nash equilibria of this game). [10pts]