Spring 2014 Quiz: 10 points Answer Key 2/19/14 Time Limit: 53 Minutes (FAS students: Teaching Assistant. Total Point Value: 10 points.

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1 Gov 40 Spring 2014 Quiz: 10 points Answer Key 2/19/14 Time Limit: 53 Minutes (FAS students: 11:07-12) Name (Print): Teaching Assistant Total Point Value: 10 points. Your Grade: Please enter all requested information on the top of this page, and put your initials on the top of every page, in case the pages become separated. You may not use your books, notes, or any calculator on this exam. If you need more space, use the extra page; clearly indicate when you have done this and label any extensions.

2 Gov 40 Quiz: 10 points Answer Key - Page 2 of 8 2/19/14 1. PART 1: ANSWER ALL MULTIPLE CHOICE QUESTIONS. For each multiple choice question please select the correct choice. There is only one correct choice, answer each question in this section. Each question worth.5 points. 2.5 points total for this section. (a) Anarchy and conflicting interests are insufficient to cause war among rational actors in the bargaining model because: (a) Anarchy is what states make of it (b) War is costly (c) It assumes states are unitary actors (d) States can effectively communicate with each other (b) What is the commitment problem of an alliance? (a) It is questionable whether member states will uphold the terms of the alliance. (b) Member states may not actually sign an alliance treaty. (c) Once an alliance treaty is signed, it is questionable whether it will be ratified. (d) It is difficult to tell which alliances really exist and which ones are fictional. (e) It is often not clear in an alliance who can declare war. (c) Imagine a Prisoner s Dilemma game is switched to be a sequential game instead of a simultaneous move game. What would the equilibrium be in this scenario (a) First player defects, second player defects (b) First player cooperates, second player defects (c) First player defects, second player cooperates (d) First player cooperates, second player cooperates (d) An outcome is Pareto efficient when: (a) one player can be made better off (b) it is impossible to make any player better off without making someone else worse off (c) no player has an incentive to unilaterally deviate from this solution (d) when each player s strategy is his or her best response to the predicted strategies of opponents (e) The following is an example of a Chicken Game: (a) Cuban Missile Crisis (b) The US-USSR arms race (c) Setting anti-deflation policy (d) Signing a global environmental treaty

3 Gov 40 Quiz: 10 points Answer Key - Page 3 of 8 2/19/14 2. PART II: ANSWER ALL GAME QUESTIONS. Find all pure strategy Nash equilibria by circling the outcome, and label the type of game the diagram represents. Answer each question in this section. 1 point each. 3 points total for this section. Figure 1: What game is this? You answer here: Prisoner s Dilemma Partner L R U (4, 10) (1, 11) You D (12, 1) (4,4). Figure 2: What game is this? You answer here: Stag Hunt Partner L R U (6,5) (1, 4) You D (4, 0) (2,2).

4 Gov 40 Quiz: 10 points Answer Key - Page 4 of 8 2/19/14 Figure 3: What game is this? You answer here: Prisoner s Dilemma Partner L R U (7, 7) (0, 9) You D (8, 0) (2,3). 3. What are the three causal logics Fearon identifies to explain war despite its cost and risk? 1 point 1. Private information and the incentives to misrepresent 2. Commitment problems 3. Indivisible issues

5 Gov 40 Quiz: 10 points Answer Key - Page 5 of 8 2/19/14 4. In order for a country to communicate information about their cost of war to an opponent, what must they do and why? 1.5 points What they must do: Send a costly signal. One example might be mobilizing troops. Why: States have incentives to misrepresent (understate) their costs of war to improve their bargaining outcomes. These incentives make communication noncredible unless it is costly.

6 Gov 40 Quiz: 10 points Answer Key - Page 6 of 8 2/19/14 5. Consider the single round bargaining game we studied in class. State A and B are engaged in a one round bargaining problem over a resource worth 100 units. State A can demand x A. If the demand is accepted by B then the resource is divided according to this rule. If it is rejected, causing war, then State A wins the entire resource with probability p =.4. If war occurs, there is a one time cost of c a = 10, c b = 20. What is the range of bargaining outcomes that both sides will prefer to war? 1 point. Let R=Resource From B s Perspective: B s payoff to war = B s payoff to bargaining R(1 p) c B = R-x 100(1-.4)-20= 100-x x=60 From A s Perspective: A s payoff to war = A s payoff to bargaining R(p) c A = x 100(.4)-10= x x=30 Therefore, the bargaining range is 30 to 60.

7 Gov 40 Quiz: 10 points Answer Key - Page 7 of 8 2/19/14 6. Consider now a similar game but where there are two rounds of bargaining. State A and B are engaged in a two round bargaining problem over a resource worth 100 units per round. In the first round, state A can demand x 1A. If the demand is accepted by B then the resource is divided according to this rule. If it is rejected, causing war, then State A wins the entire resource with probability p 1 =.2. The actor that wins the war gets the entire resource in the second period. If war occurs, there is a one time cost of c a = 20, c b = 20. If the second round is reached, the probability State A wins the entire resource following a rejected demand is p 2 =.9. Show, using the step by step analysis procedure used in class, that every demand is rejected in the first round. Make sure to explain key points of reasoning. 1 point. To solve this problem, use backward induction with A solving for the optimal offers to make B indifferent between war and peace. Let R=Resource Round 2: B s payoff to war = B s payoff to bargaining R(1 p 2 ) c B = R-x 2 100(1-.9)-20= 100-x 2 x 2 =110 This means A can keep the whole resource (x 2 =100) for itself in Round 2. (Note: we still gave full credit for using 110 here, in which case the final answer comes out to be x 1 = -50.) Round 1: B s payoff to war = B s payoff to bargaining R(1 p 1 ) c B + R(1 p 1 ) = R-x 1 + R-x 2 100(1-.2) (1-.2)= 100-x x 1 = -40 Because this is negative, there is no offer that will be accepted, and there will be preventive war in the first round.

8 Gov 40 Quiz: 10 points Answer Key - Page 8 of 8 2/19/14 EXTRA CREDIT: Prof. Tingley in lecture referenced a specific retaliatory strategy against a roommate that is dirty. What is this strategy? (.5 pt., full credit only) Leave your dirty laundry everywhere too this is a tit for tat strategy.