PoliSci30 Week 2 Notes
PoliSci30 Week 2 Notes Poli Sci 30
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Poli Sci 30
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This 9 page Class Notes was uploaded by Christine Cheung on Friday October 9, 2015. The Class Notes belongs to Poli Sci 30 at University of California - Los Angeles taught by Chwe in Summer 2015. Since its upload, it has received 25 views. For similar materials see Politics and Strategy in Political Science at University of California - Los Angeles.
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Date Created: 10/09/15
PoliSci3O Week 2 Notes Professor Chwe Strategic Form Game Focus on relevant individuals Possible alternatives for each person Assign payoffs to each outcome for each person Prediction 0 Not all alternatives have payoffs you have limited control over the outcome Prisoner s Dilemma 0 Can we unambiguously say that talking is better than not talking I Yes The payoff from talking is greater than the payoff from not talking no matter what the other person does I Talking is always better 0 Definition Strategy A strongly dominates strategy B if the person s payoff from strategy A is greater than her payoff from B regardless of what everyone else does I If A strongly dominates B pick A 0 So we predict that both will talk I Even though both would get a better outcome if neither talked Big Question 2 Why does gov t eXist What is government 0 An essential aspect of gov t even a democracy is that it can successfully threaten its own citizens with violence imprisonment etc o A gov t might eXist purely to predate on citizens I But many gov ts are liked by citizens so these gov t must offer some social benefits Answer the Prisoner s dilemma P2 doesn t pay P2 pays taxes Pl doesn t pay 0 O 4 1 P1 Pays taxes 1 4 3 3 o Incarceration solves the prisoner s dilemma with incarceration P2 doesn t pay P2 pays taxes Pl doesn t pay 10 lO 6 1 P1 Pays taxes 1 6 3 3 Why does guilt eXist 0 Because you ve been raised that way society your parents teachers etc has indoctrinated you to feel guilty for asocial behavior 0 Why did they indoctrinate you I Because they ve been indoctrinated guilt on guilt Q Why is this chain of guilt necessary I Because the punishment of guilt makes prisoners dilemma problems easier to overcome I It s the moral equivalent of incarceration Example Strictly Ballroom Ricoamp YaYa clap Ricoamp YaYa not Doug clap 10 10 5 5 Doug not 010 lO 0 For Doug clapping strongly dominates not clapping 9 we predict that Doug will clap 0 However since Doug will always clap we can eliminate the bottom row where Doug doesn t clap Ricoamp YaYa clap Ricoamp YaYa not Doug clap 10 10 5 5 0 Therefore we can determine that Rico amp YaYa will also always clap In other words we can iteratively eliminate strongly dominated strategies 0 We rst eliminate some strategies then see we can eliminate some more etc in an iterative process 0 This method is called the iterative elimination of strongly dominated strategies Example 2a 2b 2c la 8 l O O 2 3 1 2c strongly dominates 2b 1b 4 O 3 4 7 5 1c 1 9 5 2 6 8 2a 2c 1a 8 1 2 3 2 lb strongly dominates 1c lb 4 O 7 5 2a 2c 1a 8 l 2 3 3 2c strongl dominates 2a lb 4 O 7 5 1a 2 3 4 lb strongly dominates la 20 gt No more elimination Therefore we predict that 1 1b 7 5 plays b and 2 plays c Example Fashion Bob Gucci Bob Prada Bob Gucci Bob Prada Ann Gucci l l2 lll Ann Gucci l 11 lll AnnPrada lll 111 AnnPrada lll l l2 Cindy Gucci Cindy Prada Ann Prada strongly dominates Gucci So we eliminate Gucci Bob Gucci Bob Prada Bob Gucci Bob Prada AnnPrada lll 111 AnnPrada lll l l2 Cindy Gucci Cindy Prada Bob Prada strongly dominates Gucci Eliminate Gucci Bob Prada Bob Prada Ann Prada l l 1 Ann Prada l l 2 Cindy Gucci Cindy Prada Now for Cindy Gucci strongly dominates Prada Thus we are left with Bob Prada Ann Prada 1 1 1 Cindy Gucci Iterative elimination of strongly dominated strategies is a nice way of making a prediction in a game Can we say more Situations with no strong domination De nition We say that strategy A weakly dominates strategy B if the person s payoff from a strategy is at least her payoff from B regardless of what everyone else does and sometimes greater Example The Princess Bride with immunity 0 For Westley poisoning both weakly dominates poisoning V s cup 0 Poisoning both weakly dominates poisoning W s cup V choose W cup V choose V cup W poison W cup 10 100 O 10 W poison V cup 0 10 10 100 W poison both 10 100 10 100 Example 3 person game 2a 2b 2a 2b 1a 040 560 1a 006 510 1b 530 086 1b 540 040 3a 3b 2b weakly dominates 2a We can iteratively eliminate weakly dominated strategies We first eliminate strongly dominant strategies then see f1 we can eliminate some weakly dominant etc in an iterative process This method is called the iterative elimination of weakly dominated strategies Any possible drawbacks How do we make a prediction in a strategic form game Iterative elimination of strongly dominated strategies and of weakly dominated strategies 0 Strong see fashion example 0 Weak see princess bride example Drawbacks o In the iterative elimination of weakly dominated strategies sometimes the order of elimination matters I There is an element of arbitrariness o Iterative elimination of strongly dominated strategies has no order of elimination requirement 0 Example 1 1a strongly dominates lb 2 2a weakly dominates 2b 2a la 8 5 3 la strongly dominates 1c lPil o The order matters for weak domination because in strong domination one option will ALWAYS be better than the other but in weak domination sometimes there s a tie so it can ip around 0 So when you use iterative elimination of weakly dominated strategies just be aware that some arbitrariness is possible Are there any other problems with this strategy 0 There might not be any strong or weak domination o Footloose example Chuck swerve Chuck doesn t Ren Swerve O O 10 10 Ren doesn t 1010 100 100 o No strategies are strongly dominated o No strategies are weakly dominated I So no iterative elimination possible 0 Maybe we can make a prediction I Instead of deducing what people will play just go ahead and make a prediction and then see if it makes sense Chuck swerve Chuck doesn t Ren Swerve O O 10 10 Ren doesn t 10 10 100 100 There are 4 possible predictions 0 A Ren swerves Chuck swerves o B Ren swerves Chuck doesn t o C Ren doesn t Chuck swerves o D Ren doesn t Chuck doesn t A prediction makes sense if given the prediction each person wants to play according to the prediction I A No doesn t make sense I B Yes does make sense I C Yes I D No Strategy Pro les A strategy pro le is a speci cation of what each person s strategy is 0 It s a possible prediction 0 In a 2 person game a strategy pro le is a pair of strategies 0 In a 3 person game triple of strategies etc o In the foot loose example there are 4 possible pro les A strategy pro le is a Nash Equilibrium if no person wants to choose some other strategy deviate given what everyone else does 0 A Nash Equilibrium makes sense in that if it is predicted then everyone wants to follow the prediction assuming it is true 0 A Nash Equilibrium is a selfful lling prophecy o In order to see if a prediction is a NE then look at their other options to see if there are any better ones If not then it IS a NE Footloose example Chuck swerve Chuck doesn t Ren Swerve O O 10 10 Ren doesn t 10 10 100 100 0 There are 4 strategy pro les I A Ren swerves Chuck swerves 9 not a Nash eq Because both could bene t from deviating from this prediction I B Ren swerves Chuck doesn t 9 Nash eq No one Will gain from NOT doing this I C Ren doesn t Chuck swerves 9 Nash eq No one Will gain from NOT doing this I D Ren doesn t Chuck doesn t 9 not a Nash eq Both would de nitely bene t from deviating from this prediction 0 THEREFORE our prediction is that one person swerves and the other doesn t 0 We can t predict Which person Will swerve Arms Race example CCCP arm CCCP not US Arm 10 10 10 5 US not 5 10 00 0 Nash eq Us not CCCP arm and US arm CCCP not I In an arms race there Will be a hegemon No one arming is not an equilibrium since someone Will want to arm a power vacuum but if both arm someone Will back down Prisoner s Dilemma Presents example Beatrice doesn t Beatrice gives Arnold doesn t O O 4 1 Arnold gives 1 4 3 3 0 NE Arnold doesn t Beatriz doesn t o This example can also be iteratively eliminated Beatrice doesn t Beatrice gives Arnold doesn t O O 4 l 1 Arnold not giving strongly dominates giving 1 790 1 A 2 2 1 LLLLULU KLV V0 1 I39 J J Example Strictly Ballroom Rico amp YaYa clap Rico amp YaYa not Doug clap 10 10 5 5 Doug not 5 5 00 0 The only NE is Doug claps Rico amp YaYa clap I This is the same prediction we got from iterative elimination of strongly dominated strategies How do I nd all pure strategy Nash equilibria of a game Check each strategy pro le 0 If some person can gain by deviating given what everyone else does then the strategy pro le is NOT a NE A Nash Equilibrium is a strategy pro le from which no one can gain by deviating Is there a way to nd NE without looking at every possible strategy pro le YES A given strategy is a Nash equilibrium if no person wants to deviate given what everyone else does It s a Nash equilibrium if each person is playing a best response given what everyone else does 0 Example Arms Race CCCP arms CCCP not US Arm 1010 105 US not 5 10 00 0 Use to indicate US s best response given what CCCP does 0 Use to indicate CCCP s best response 0 NE are pro les which have both and Example Giving Presents Beatrice doesn t Beatrice gives Arnold doesn t 0 0 4 1 Arnold gives 1 4 3 3 o The best strategy is neither of them give Example strictly ballroom Rico amp YaYa clap Rico amp YaYa not Doug clap m m 5 Best response is both Clap Doug not 5 5 0 Q Example Fashion Bob Gucci Bob Prada Bob Gucci Bob Prada Ann Gucci 1l2 11i Ann Gucci 111 11i Ann Prada la 17 i la l 1 Ann Prada la 17 i la la 2 Cindy Gucci Cindy Prada o The NE is Ann Prada Bob Prada Cindy Gucci
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