Problem Set 2 Answers

Problem Set 2 Answers - PPS55 Spring 2008 Problem Set#2...

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PPS55: Spring 2008 Problem Set #2 - ANSWERS 1. King Me! Larry King is planning to invite Mitt Romney, Hilary Clinton and Dennis Kucinich to come on his show and talk about their platforms. For complicated reasons involving career advancement, reputation of ones’ party, and personal feelings about the individuals involved, let’s assume that the payoffs are those depicted on the following game tree: (a) Suppose that Larry will sequentially invite Romney, then Clinton, then Kucinich. What should Romney do? Show your work!!! Romney should accept. Note that to solve a sequential game we use backwards induction, so you simply prune the tree from right to left, determining what an individual would do if faced with that choice. Thus strategies like maximin that one might use in a simultaneous game are completely irrelevant. Each party knows exactly where they are in the tree when they make their choice, and can see what the others will do once their choice is made. For a similar reason the idea of a dominant strategy is also irrelevant in a sequential game. (b) Would it make a difference if Clinton could commit to accepting or declining before Romney makes his choice? Briefly explain why or why not. (Hint: If Clinton commits before Romney 4, 4, 5 Romney Kucinich Clinton Accept Accept Accept Accept Accept Accept Accept Decline Decline Decline Decline Decline Decline Decline 6, 3, 1 3, 1, 7 1, 2, 3 2, 6, 6 7, 7, 2 5, 5, 8 8, 8, 4
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makes his choice, this is analytically equivalent to her going first, Romney second and Kucinich third). Yes, it would. If Clinton can commit to declining, she forces Romney to choose between a payoff of 5 if he declines and 3 if he accepts. When he chooses to decline, they actually both do better than when she didn’t commit (both get 5 instead of 4). What she is actually doing by committing is telling Romney that she will forgo the payoff of 6 from (Decline, Accept, Accept) in order to get to an outcome that is better than the one in part a. She makes it safe for Romney to decline – note on the tree above that if she didn’t commit and he chose decline, she’d choose accept and he would get a payoff of only 2. If the outcome is still confusing, redraw the tree with Clinton moving first, then Romney and Kucinich. You’ll see that the best outcome is for Clinton and Romney to decline. Here is the redrawn tree: 2. The Forest or the Trees?
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This note was uploaded on 04/22/2008 for the course PUB POL 55 taught by Professor Vigdor during the Spring '08 term at Duke.

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Problem Set 2 Answers - PPS55 Spring 2008 Problem Set#2...

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