Asymmetric information bargaining. It is April 2024 and the Republicans have a slim majority in the House of Representatives. Both parties want to pass an aid package, but Republicans prefer a smaller amount of aid for Ukraine than President does. In the game below, the Republicans are trying to pass a bill with a minimal amount of aid for Ukraine, while still getting the President to sign it. The Republicans, R, pass legislation with an amount of aid to Ukraine, u > 0; assume that the aid to other countries is fixed and therefore not directly part of the payoff. The President P, can accept the legislation by signing it into law or he can veto it. The pavoffs for signing reflect the fact that (1) the President has a minimum value of aid that he would accept (reflected by d), (2) the President gets more utility per dollar of aid than it costs Republicans (2u), and (3) Republicans have a maximum level of aid they would be willing to provide (r). Both the Republicans and the President are expected utility maximizers. (a) Suppose that d (R IS 30, where both values are common knowledge. What are the subgame-perfect equilibria of the game? [There are multiple. Make sure you list all of them.] Now suppose that d is private information held by the President. Republicans believe that d is distributed uniformly between 20 and 100. To calculate the Republican's optimal offer, you will need to calculate the probability that the President signs. E.g., If u = 30, the probability of Sign is Pr(2-30 > d) = 0.5. (b) For any given u, what is the probability the President signs? () For a high enough r (like r = 80), what is expected payoff to Republicans of offering u? For a high enough r (like r 80), what is the subgame perfect Nash equilibrium? (You should answer this with calculus; alternatively you can provide a very accurate graph using Desmos; partial credit for trying different numerical values.) [Be sure to specify full strategies.| What is the probability that the President vetoes the legislation in equilibrinm? Explain what this has to do with the efficiency of bargaining with asymmetric information