6. Two swimmers players 1 and 2 are to participate in a runoff. Each player has the option of using a performanceenhancing 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 I] s [ITO 111 n 1]1 0?0 (a) Analyze this game and explain why an antidoping policy is needed. [5pts] (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 doping player who is caught by ICC will lose the game and pay a penalty of b > U) and the 100 in this case will improve its image. The payoffs of the threeplayer game are as follows. S I] S 11 s 1b,171 1b?131 s 1,104 1:170 n 1?1]0 0,0,0 'n 11104 01010 t1 t2 1. Explain why it is not a Nash equilibrium for IOC 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]