ps30 - Hiroki Takeuchi hirokit@ucla.edu PS 30: Sections 1I,...

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hirokit@ucla.edu PS 30: Sections 1I, 1J, & 1K Practice Problems for Midterm This is designed to give you more problem sets, which will help prepare for final and, more importantly, understand basic game theory. In short, these are “practice problems for midterm,” rather than “practice midterm.” 1. Two candidates, Incumbent and Challenger, are competing for the same office. Each faces a choice of whether to run a positive campaign emphasizing their own accomplishments or a negative campaign that emphasizes their opponent’s shortcomings. If one runs a negative campaign and the other runs a positive campaign, the one that ran the negative campaign will win. If they both run the same kind of campaign, Incumbent will win. Winning the election is worth 5 units of payoff to either candidate. Neither candidates likes running a negative campaign, however. Each candidate loses 2 units of payoff if they run a negative campaign. (a) Suppose that Challenger decides her campaign strategy first. Draw a game tree and solve it using backwards induction. What do you predict to happen? Transform the game tree into a strategic form. Find PSNE and SPE. (b) Now suppose that Incumbent decides her strategy before Challenger does. Draw a game tree and solve it. What do you predict to happen? Transform the game tree into a strategic form. Find PSNE and SPE. (c) Now suppose that Challenger and Incumbent decide their strategies simultaneously. Draw a matrix and find all Nash equilibria (PSNE and MSNE if they exist). What is the probability of Challenger winning? (d) Suppose again that Challenger moves first, but now Incumbent is “extra ethical” and loses six (rather than two) units of payoff from running a negative campaign. Draw a game tree that incorporates this change. What will Challenger choose? Transform the game tree into a strategic form. Find PSNE and SPE. (e) Suppose that Challenger and Incumbent decide their strategies simultaneously and Incumbent is “extra ethical.” Draw a matrix and find all Nash equilibria (PSNE and MSNE if they exist). 1
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ps30 - Hiroki Takeuchi hirokit@ucla.edu PS 30: Sections 1I,...

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