6. 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 n 0,0 1, -1 n -1, 1 0,0 (a) Analyze this game and explain why an anti-doping policy is needed. [5pts] (b) Suppose the international olympics organization (IOC, player 3) intervene. Let us further assume that IOC 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 IOC will lose the game and pay a penalty of b > 0, and the IOC in this case will improve its image. The payoffs of the three-player game are as follows. S n S n S -1 - b, 1, 1 -1 - b, 1, 1 S 1, -1 - b, 1 1, -1,0 n -1, 1,0 0,0,0 n 1, -1 - b, 1 0, 0,0 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]