3. Time is running out on raising the national debt limit. If the limit is not raised, the United States will not be able to pay its debt and the financial markets will be more likely to panic as time goes on. One key issue is that the Republicans want to lower spending on domestic programs while the Democrats oppose this. Both parties are now locked in a brinkmanship contest to see who will \"blink\" first. A second key issue is whom the voters hold responsible for the deadlock. If the voters blame one of the parties, it will hurt that party in next year's presidential election. The game tree below models aspects of the situation. Republicans (R) begin the game by deciding whether to force a shut down or compromise. If R decides to force a shutdown, the voters blame R with probability r (and the voters blame D with probability 1-r). Who the voters blame affects the parties' payoffs in the event of a financial disaster. Assume that the probability that the voters blame R is r = 0.25 in parts (a)-(d). (a) What is D's resolve in the brinkmanship game starting at node [1]? What is R's resolve in the brinkmanship game starting at node [1]? (b) What is the subgame-perfect equilibrium of the subgame starting at node [1]? (c) What is the subgame-perfect equilibrium of the subgame starting at node [2]? (d) Recall that the probability that voters blame R is = 0.25. Does R compromise or shut down the government in the equilibrium of the game? What is R's payoff to shutting down the government in the subgame-perfect equilibrium of the game? e e more likely the voters are to blame R for a financial panic (i.e., the higher r is), the lower R's Th likely th bl R f fi ial ic (i he high is), the 1 R' payoff to shutting down the government. For what values of r will shutting down the government be equilibrium behavior for R? Payoff Key: ( R's payoff, D's payoff) 8, -3 -2, 12 8, -3 -2. 12 8, -3 quit quit quit quit quit Z firm firm Z firm firm firm -7, -48 [1] A disaster disaster disaster disaster 0,0 blame D 20% 40% 60% 80% -7, -48 -7, -48 compromise -7, -48 -7, -48 Z force shut down Page 4 of 7 8, -3 -2, 12 8, - -2. 12 8, -3 blame R (r) quit quit quit quit quit firm firm firm firm firm -12, -8 D [2] disaster disaster disaster disaster 20% 40% 60% 80% -12, -8 -12,-8 -12, -8 -12, -8