Question 2: Consider the strategic interaction between a policy maker and a special interest group (SIG). The SIG moves first and must choose whether to approach the policy maker or stay silent. The policy maker moves second and must choose whether to adopt policy a or policy b. There are two possible states of the world: A and B. The state of the world determines which policy is most efficient. In other words, policy a is most efficient in state A and policy b in state B. The SIG knows the state of the world, but the policy maker does not. The policy maker has prior beliefs that the state of the world is A with probability The policy maker gets a payoff of G if he implements the most efficient policy, and 0 otherwise. The SIG also cares about efficiency, but on top of that has ideological preference for policy b. In short, the SIG's payoff is as follows: - G+K if the policy maker implements policy b in state B - K if the policy maker implements policy b in state A - G if the policy maker implements policy a in state A - 0 if the policy maker implements policy a in state B In addition, approaching the policy maker is costly for the SIG: if SIG chooses to approach the legislator it must pay a cost C. To sum up, the timing of the game is as follows 1. SIG observes the state of the world 2. SIG chooses whether to approach the policy maker or stay silent 3. Policy maker chooses policy a or b Under which conditions does this game have a separating equilibrium in which the SIG chooses to approach the policy maker in state B and to stay silent in state A ? (hint: remember to follow the three steps, and try to be as precise as possible)