Final_Exam_Review_Key

.pdf

School

New York University *

*We aren’t endorsed by this school

Course

700

Subject

Economics

Date

Jan 9, 2024

Type

pdf

Pages

Uploaded by DukeDanger12067

1 Introduction to International Relations Spring 2023 Final Exam Practice Questions Key Below you can find a number of practice problems of similar style, content, and difficulty to what might appear on your final exam (these actually may be somewhat more difficult than the exam). As with the midterm review, this set of problems is not exhaustive of the content you are liable for but meant to guide your study in the right direction. As the final exam is cumulative, questions may be drawn from lectures/readings/recitations from any point in the semester – although there will be a natural bias towards content arising in the second half of the course. Answers to all questions should be short and to the point, one or two sentences generally being sufficient. 1. What is the fundamental puzzle of war, according to Fearon? What five assumptions must hold to generate this puzzle, and which three of these assumptions does Fearon favor as his rationalist explanations for war? The fundamental puzzle of war is that it occurs despite its risks and costs; an ex ante bargaining range should exist. This result holds under the assumptions of rationality, risk neutrality/aversion, complete information, binding contracts, and perfect issue divisibility. The last three of these, when loosened, are Fearon’s rationalist explanations for war. 2. What is a Nash equilibrium? What is a best response? What is the name of the technique for solving extensive form games of complete information (the type of game tree we have seen most frequently in class)? A Nash equilibrium is a simultaneous best response. A best response is when, holding the behavior of everyone else constant, you are doing what is best for you. Backwards induction. 3. One of the first major formal models of conflict introducing domestic politics to explain patterns of war was Fearon’s 1994 model of audience costs. Under what conditions do audience costs arise? Are threats more credible when audience costs are high or low? Are threats made more frequently when audience costs are high or low? Audience costs arise when a leader makes a threat and then backs down when resisted. Threats are more credible when audience costs are high, and threats are made more frequently when such costs are low.

2 4. Consider the following model of aid-for-policy deals in which Leader 1 offers some ? resources (out of the budget ? 1 ) to Leader 2 (in addition to their budget of ? 2 ) in return for some (public good-type) policy worth 𝜎 1 utility to the winning coalition of Leader 1 (? 1 ) and a (public bad-type) disutility of 𝜎 2 to the winning coalition of Leader 2 ? 2 . This offer can be either accepted or rejected, rejection leading to the entire leader’s budget being spent on private goods for their coalition and acceptance leading to the deal described above. a) Under what condition does Leader 2 accept the aid-for-policy deal? Solve this condition for ? 2 . Are large or small coalition leaders more likely to accept a given aid-for-policy deal? Leader 2 accepts when 𝑅 2 +𝑥 ? 2 − 𝜎 2 ≥ 𝑅 2 ? 2 , i.e. ? 2 ≤ 𝑥 𝜎 2 . Small coalition leaders are more willing to accept. b) Given the above, what is the optimal accepted offer that Leader 1 can make to Leader 2, i.e., that which leaves them with the largest amount of resources for themselves? Call this value ? ∗ . Are large or small coalition leaders cheaper to buy off? In other terms, conditional on receiving aid do large or small coalition leaders get more? Leader 1 makes Leader 2 indifferent, keeping the surplus for themselves: ? ∗ = ? 2 𝜎 2 . Small coalition leaders are cheaper to buy off; conditional on receiving aid large coalition leaders get more. c) Under what conditions is Leader 1 willing to make such an accepted offer? Solve this condition for ? 1 and substitute in the optimal offer found in part b. Are large or small coalition leaders more likely to provide aid? Leader 1 makes such an offer when 𝑅 1 −𝑥 ∗ ? 1 + 𝜎 1 ≥ 𝑅 1 ? 1 ; i.e. ? 1 ≥ 𝑥 ∗ 𝜎 1 ; i.e. ? 1 ≥ ? 2 𝜎 2 𝜎 1 . Large coalition leaders are more likely to provide aid.

3 d) Suppose that a mutually agreeable aid-for-policy deal has been struck between Leader 1 and Leader 2 as above. Now consider the distributional consequences of the aid-for-policy deal by filling out the following grid (what do segments of the population get under acceptance or rejection, and are they better or worse off? The leader’s coalition are members of their winning coalition, while the population is not within the coalition). 5. Suppose that we are interested in rationally updating our beliefs in a hypothesis ( 𝐻 ) given some evidence (? ); i.e. we want to know Pr (𝐻|?) . a) Write down the Bayes’ Rule expansion of this conditional probability supposing that there are only two relevant hypotheses (i.e. 𝐻 and ¬𝐻) . Pr(𝐻|?) = Pr(?|𝐻) Pr(𝐻) Pr(?|𝐻) Pr(𝐻) + Pr(?|¬𝐻) Pr(¬𝐻) b) Show that if the evidence is uninformative (the probability of either hypothesis is the same under the evidence) that beliefs do not update (the posterior equals the prior). Pr(𝐻|?) = 𝑎 Pr(𝐻) a Pr(𝐻) + a Pr(¬𝐻) = 𝑎 𝑎 Pr(𝐻) Pr(𝐻) + Pr(¬𝐻) = Pr(𝐻) 1 = Pr(𝐻) Actor(s) Utility if Accepted Utility if Rejected Beneficiary of Deal? Leader 1 ? 1 − ? ∗ ? 1 + 𝜎 1 ? 1 ? 1 Yes Leader 2 ? 2 + ? ∗ ? 2 − 𝜎 2 ? 2 ? 2 Yes Leader 1 Coalition ? 1 − ? ∗ ? 1 + 𝜎 1 ? 1 ? 1 Yes Leader 2 Coalition ? 2 + ? ∗ ? 2 − 𝜎 2 ? 2 ? 2 Yes Leader 1 Population 𝜎 1 0 Yes Leader 2 Population −𝜎 2 0 No

4 c) Show that if beliefs are dogmatic (the prior belief in the hypothesis is either zero or one) that no updating occurs (the posterior equals the prior). Pr(𝐻|?) = Pr(?|𝐻) × 0 Pr(?|𝐻) × 0 + Pr(?|¬𝐻) × 1 = 0; Pr(?|𝐻) × 1 Pr(?|𝐻) × 1 + Pr(?|¬𝐻) × 0 = 1 d) Suppose that the probability of the evidence under ¬𝐻 is zero while the probability of the evidence under 𝐻 is positive. What is the posterior belief in 𝐻 after observing this ‘critical test’ ? ? Pr(𝐻|?) = Pr(?|𝐻) Pr(𝐻) Pr(?|𝐻) Pr(𝐻) + 0 × Pr(¬𝐻) = Pr(?|𝐻) Pr(𝐻) Pr(?|𝐻) Pr(𝐻) = 1 6. When solving for a Perfect Bayesian Equilibrium of the form we have encountered in class, what are the three essential steps? Check the consistency of posterior beliefs given the presumed behavior of types. Check the best response of the actor with incomplete information given these beliefs. Check the best responses of each type of the other player, given the behavior of the actor with incomplete information.

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version