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PoliSci30 Midterm Review!

by: Christine Cheung

PoliSci30 Midterm Review! Poli Sci 30

Christine Cheung
GPA 4.0

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About this Document

This is a comprehensive review of each week of Professor Chwe's PoliSci30 lectures. Includes detailed examples with exact, step-by-step explanations of how to do each type of problem we encountered...
Politics and Strategy
Study Guide
Chwe, PoliSci30, simple model, strategic form game, Game Theory, Nash equilibrium, mixed strategy, Nash, Probability, iterative elimination, domination, strategy, strongly dominated strategies, weakly dominated strategies, backward induction
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This 14 page Study Guide was uploaded by Christine Cheung on Sunday November 1, 2015. The Study Guide belongs to Poli Sci 30 at University of California - Los Angeles taught by Chwe in Summer 2015. Since its upload, it has received 58 views. For similar materials see Politics and Strategy in Political Science at University of California - Los Angeles.


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Date Created: 11/01/15
PoliSci30 Midterm Study Guide Week 1 Review: Models • Models are purposefully simplified descriptions of something • Purposes o Illustrating, demonstrating, or testing things o “What if?” situations o Planning purposes—lower costs o Persuasion/argument o Analogize • Using models in this class o Models are common for social science o Game theory is one of the simplest models o How to model—don’t mix up a model and the real world! • Game Theory o Emphasizes choice ▯ This is why people do what they do o A way to model why people make the choices they make The Simplest Model of individual choice • Steps o Identify the relevant individual o Write down her possible alternatives o Identify the one with the highest payoff (or utility) • Example: Fruit o Annie chooses between: Apple (8), Orange (5), Blueberry (2), Raspberry (12) o She will choose raspberry because it has the highest payoff! • Notes o Simple model does not assume people are “materialistic” or care only about cash o Assumptions with this model ▯ There is only one person making a choice • And that person’s choice is not affected by anyone else’s! • That choice is selfish! They will pick whatever is best for them ▯ No “framing” or “contextual” effects • Effects of comparison to context that cause people to change their mind for different circumstances ▯ No involuntary behavior ▯ No behavior based on “drives” • Ex: Yesterday I ate a burrito and later (for unrelated reason) I got a stomachache. I know that eating a burrito today won’t make me get another stomachache, but I just CAN’T ▯ No “rule-based” behavior • Particular personal rules that people do—I can’t buy the same ticket twice o Limitations ▯ Your preferences shouldn’t change according to the simple model, but circumstances can make you change your mind! ▯ Changing your mind is a violation of the simple model! Big Question #1: What does rationality mean? • Game theory: rationality is behavior that is consistent with the simple model • Key ideas: o We can’t be judgmental about what people “should" want/do o It’s more about consistency of choice than right/wrong • Game theorists look at the world in terms of individuals who are each making choices • Apply the simple model of rational choice! o 1 focus on the relevant individual o 2 write down possible alternatives o 3 identify the one with the highest payoff Strategic Form Game • New model of rational thought, for when the simple model is inadequate • Characteristics o More than one person o Each person chooses among a set of alternatives o Each outcome has a payoff for each person ▯ Outcome: pair of strategies, a combination of what both players do • Example: Murder by numbers o Justin and Richard both need to decide to talk or not talk Justin Talks Justin Doesn’t Richard Talks 0 0 10 -10 Richard Doesn’t -10, 10 5, 5 • Major Types of Strategic Form Games o Chicken ▯ Ex: Footloose tractor game Chuck Swerve Chuck not Ren Swerve 0, 0 -5, 10 Ren doesn’t 10, -5 -10, -10 o Matching Pennies ▯ Ex: The Princess Bride Vizzini drinks W’s cup V drinks his cup Westley poison his cup 10, -10 -10, 10 W poison V’s cup -10, 10 10, 10 o Cooperation Problem/ Prisoner’s Dilemma ▯ Ex: Murder by numbers Justin Talks Justin Doesn’t Richard Talks 0 0 10 -10 Richard Doesn’t -10, 10 5, 5 o Coordination Problem ▯ Players have the same goal, but they need to get there together ▯ Ex: driving on the same side of the street John Right John Left Tim Right 3 3 -3 -3 Tim Left -3 3 3 3 • Two Players, 3 choices (Rock Paper Scissors) P2 Rock P2 Paper P3 Scissors P1 Rock 0,0 -1, 1 1, -1 P1 paper 1, -1 0,0 -1, 1 P3 Scissors -1, 1 1, -1 0, 0 • Three player strategic form game Bob Gucci Bob Prada Bob Gucci Bob Prada Ann Gucci 0, 9, -5 0, 5, 1 Ann Gucci 0, 9, 9 0, 5, 1 Ann Prada 9, 5, 1 9, 9, 9 Ann Prada 9, 5, 1 9, 9, -5 Cindy Gucci Cindy Prada o Notes: Players 1 and 2 are set up like normal; player 3 is along the bottom o You create multiple matrixes for the number of choices that player 3 has! Week 2 Review: Strategic form game steps: • Focus on relevant individuals • Possible alternatives for each player • Assign payoffs to each outcome, for each person • Prediction? o Not all alternatives have payoffs—you have limited control over the outcome Big Question #2: Why does government exist? • What is gov’t o An essential aspect, even in democracy, is the ability to successfully threaten its own citizens with violence, imprisonment, etc. o It might exist purely to predate on citizens • Government works because incarceration solves the Prisoner’s Dilemma! P2 doesn’t pay P2 pays taxes P1 doesn’t pay -10 , -10 -6, -1 P1 Pays taxes -1 -6 3 3 • Why does guilt exist? o Society has indoctrinated you to feel guilty for asocial behavior o Chain of guilt is necessary because it makes the prisoner’s dilemma problems easier to overcome ▯ Moral equivalent of incarceration Making Predictions in Strategic Form Games • Iterative elimination of strongly dominated strategies o Strategy A strongly dominates Strategy B if the person’s payoff from A is always greater than B, regardless of what everyone else does • Ex: Strictly Ballroom o But, there are still situations where there are no strong domination… • Iterative elimination of weakly dominated strategies o Strategy A weakly dominates Strategy B if the person’s payoff from A is always greater than or equal to her payoff from B, regardless of the other person • Ex: 3 person game 2a 2b 2a 2b 1a 0, 4, 0 5, 6, 0 1a 0, 0, 6 5, 1, 0 1b 5, 3, 0 0, 8, 6 1b 5, 4, 0 0, 4, 0 3a 3b 2b weakly dominates 2a • IMPORTANT! o While doing iterative elimination, it’s important to compare the correct choices!! o Player 1: compare up and down (0 and 5; 5 and 0; 0 and 5; 5 and 0) 2a 2b 2a 2b 1a 0, 4, 0 5, 6, 0 1a 0, 0, 6 5, 1, 0 1b 5, 3, 0 0, 8, 6 1b 5, 4, 0 0, 4, 0 3a 3b o Player 2: compare side to side (4 and 6, 0 and 1, 3 and 8, 4 and 4) 2a 2b 2a 2b 1a 0, 4, 0 5, 6, 0 1a 0, 0, 6 5, 1, 0 1b 5, 3, 0 0, 8, 6 1b 5, 4, 0 0, 4, 0 3a 3b o Player 3: compare the same position in both matrixes (0 and 6, 0 and 0, 0 and 0, 6 and 0) 2a 2b 2a 2b 1a 0, 4, 0 5, 6, 0 1a 0, 0, 6 5, 1, 0 1b 5, 3, 0 0, 8, 6 1b 5, 4, 0 0, 4, 0 3a 3b o Note: The order of elimination matters for weakly domination because when there’s a tie, there is some arbitrariness in the order ▯ Whereas in strong domination, one strategy will ALWAYS be better Strategy Profiles & Nash Equilibrium • A strategy profile is a specification of what each person’s strategy is o A possible prediction for a move • Nash Equilibrium (NE): a characteristic of a strategy profile, achieved if no person wants to deviate (chose another strategy) given what the other person does o Self-fulfilling prophecy o Situation of everyone’s best response • Ex: Arms Race o Underline the best possible moves for each comparison (using same comparison guidelines as in iterative elimination), then whichever has both players underlined is Nash Equilibrium! CCCP arm CCCP not US Arm -10, -10 10, -5 US not -5, 10 0, 0 o NE: (US not, CCCP arm) and (US arm, CCCP not) • Finding all pure strategy Nash Equilibrium o Check each strategy profile: if one person can gain from deviating, then it’s not NE! Week 3 Review: Strategic Form Game: • Focus on relevant individuals • Write down alternatives • Assign payoffs • Prediction o Iterative elimination of strongly and/or weakly dominated strategies o Nash equilibrium (situation of best response) Big Question #3: Why is it difficult to overthrow a regime, even if it is widely hated? • Issue of assurance o It’s not easy to get everyone to protest all at once, and you have to be pretty positive everyone is going to show up! P2 protests P2 stays home P1 protests 10, 10 -5, 0 P1 stays home 0, -5 0, 0 Big Question #4: How can a single person create large social change? • Rosa Parks example o By making one person’s payoff to make them courageous or reckless, her -100 changes to 1 P2 protests P2 stays home P1 (Rosa Parks) protests 10, 10 1, 0 P1 (Rosa Parks) stays home 0, -100 0, 0 • BUT: how many people do you have to repress in order to prevent protest? o Reward the person who stays home P2 protests P2 stays home P1 protests 10, 10 -5, 0 P1 stays home 15, -100 15, 0 o Punish the person who protests P2 protests P2 stays home P1 protests -40, 10 -5, 0 P1 stays home 0, -100 0, 0 Matching Pennies: What about situations with no Nash Equilibrium? • Ex: Penalty Kick Striker East Striker West Keeper East 1, 0 0, 1 Keeper West 0, 1 1, 0 • You have to find the probability of each player choosing each strategy [q] [1-q] Striker East Striker West [p] Keeper East 1, 0 0, 1 [1-p] Keeper West 0, 1 1, 0 • Then, find the Expected Utility (EU) of each player’s strategies EU KeeperEast) = 1(q) + 0 (1-q) = q + 0 = q EU KeeperWest) = 0(q) + 1(1-q) = 1-q EU (East)= 0(p) + 1(1-p) = 1-p Striker EU Strikerest)= 1(p) + 0(1-0)= p • Set Expected Utilities for each player equal to each other to find switchover points (p and q) EU (East) = EU (West) Keeper: Striker: q=1-q 1-p = p 2q=1 1 =2p q= ½ p= ½ • Thus, you can determine your mixed NE Notes • We know how to write down a strategic form game • How do we make a prediction? o Iterative elimination of strongly or weakly dominated strategies o (Pure strategy) Nash equilibrium o Mixed strategy Nash equilibrium • That’s it! o John Nash proved in 1950 that these methods can find predictions for any type of strategic form game • However, note that in a strategic form game, we implicitly assume that each person chooses independently o When choosing your actions, you can’t respond to the actions of others o People choose their actions “simultaneously” o But in many situations (chess, tic-tac-toe), you respond to the actions of others ▯ People move in sequence ▯ To model these, we use an extensive form game Week 4 Review Extensive form game • Main ideas o Subgame perfection ▯ A NE is subgame perfect if in every subgame, people’s actions correspond to a NE in that subgame (No non-credible threats) o What is a strategy ▯ To specify a person’s strategy you have to write down an arrow from all of her nodes • A strategy is a complete contingent plan • Example: Kidnapping o A kidnapper can choose to kidnap or not, if kidnap, the family can pay or not. Family Pay 10, -20 Kidnap Kidnapper Not -5, -100 Not 0, 0 This is an extensive form game (tree) o Step 2: assign utilities o This is an extensive form game! ▯ It has decision nodes (labeled with the person who chooses) ▯ Branches from each decision node labeled by the possible choices at that node ▯ Terminal nodes with payoffs o How do we make a prediction? ▯ Try to make it like a strategic form game If Kidnapped Pay Not Kidnap 10, -20 -5, -100 Not 0, 0 0, 0 ▯ Two NE: (kidnap, if kidnapped pay) and (not, if kidnapped not) ▯ In graphic terms, the chart represents the kidnapper choosing the top then bottom branch (rows), then the family choosing the top then bottom branch (columns) o We have two NE, but one of them is “sketchy” ▯ The (not, if kidnapped not) is sketchy Family Pay 10, -20 Kidnap Kidnapper Not -5, -100 Not 0, 0 ▯ In this NE, the family never chooses (because the kidnapper doesn’t kidnap) • Paying weakly dominates not paying ▯ It’s sketchy because not paying is a non-credible threat • If the family does choose, it will choose to pay o Another way to think about this is that once the kidnapper kidnaps, the family plays a subgame Subgame ▯ We can think of this subgame as a game in itself ▯ The family’s action in this subgame is not a NE of the subgame: the family can gain from deviating o What about the other NE (kidnap, if kidnapped pay) o IF the family gets to choose, it WILL choose to pay ▯ This is a credible choice Family Pay 10, -20 Kidnap Kidnapper Not -5, -100 Not 0, 0 o We have 2 NE (kidnap, if kidnapped pay) and (not, if not kidnapped not) ▯ In the first, the family’s action is a NE in the subgame • It’s credible • This NE is called a subgame perfect NE ▯ In the second, the family’s action is not a NE in the subgame • This isn’t credible • This NE is NOT a subgame perfect NE • Subgame perfect: occurs in an extensive form game IF in every subgame of the original game, people’s actions correspond to a NE of that subgame o In any extensive form game, there might be several NE ▯ Some are subgame perfect, some aren’t o In a subgame perfect NE, there are no non-credible threats ▯ It’s a matter of judgment whether subgame perfect NE are more reasonable than non-perfect NE—sometimes non-credible threats are reasonable, sometimes not Three main ideas in extensive form game • Subgame perfection o A NE is subgame perfect if in every subgame, people’s actions correspond to a NE in that subgame (no “non-credible threats”) • What is a strategy? o To specify a person’s strategy, you have to write down an arrow from all of her nodes o A strategy is a complete contingent plan! • Backward induction o To find subgame perfect NE, the method of backward induction is faster Backward induction • In an extensive form game, this is the easiest way to find Subgame Perfect Nash Equilibrium (SPNE) • Start with the end of the game, then figure out each person’s best response and move backward • Ex: Prom o Thus, SPNE is (not ask, not; refuse) Week 5 Review Extensive Form Games with Ties▯ more than one SPNE! Big Question #5: Is it ever worthwhile to purposefully limit your own actions? • Yes • If you were the only person in the world, you’d never want to • But sometimes it’s more beneficial to you if there’s someone else involved • Ex: Dr. Strangelove • These two games can be combined to see all the possibilities, starting out with whether or not the CCCP will decide to bind itself to using the doomsday device


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