updated 1/2/14
Poli Sci 30
Politics and Strategy
Online Hybrid Version
Winter 2014
Professor Kathleen Bawn
[email protected]
Bunche 3363
Office hours Th 2-4
Welcome to Poli Sci 30!
Poli Sci 30 is an introductory course in game theory, aimed at Politi
LESSON 39
updated 5/28/13
Lesson 39: Unreasonable NE?
We found three NE when we solved the Superintendent-Community Leader Game in
normal form.
Comm Leader
PC if Q, PC if unQ
PC if Q,N if unQ
N if Q,PC if unQ
N if Q, N if unQ
-4
-4
0
0
NE-2
Sup
Q
-7
-7
0
Lesson 36
Lesson 36: Interpreting MSNE
Recap: Compare Cops & Robbers Version 1
Robbers
At Work
-5
Cops
On Beat 2
Home
0
1
5
Donuts -5
5
NE to this game is cops are on beat with prob , robbers are active with prob 4/11.
0
Outcomes: all four things may happ
Lesson 34
Unit 10: Mixed Strategies, Part 2
Lesson 34: Games with PSNE and MSNE
Basic system for finding NE in mixed strategies.
1. Use variables to represent probabilities associated with each player pure strategies.
2. Write out the expected values of p
Lesson50
Lesson 50: Multiple Equilibria in the Repeated PD
50A. Tit-for-Tat
50B: Folk Theorem
Another famous strategy: Tit-for-tat. I start out cooperating and then do whatever
you did in the last round
- Single defection gets a single-period punishment.
Lesson 51
Lesson 51: What do we learn from the Repeated PD?
51A. TFT and Axelrods Tournament
51B. Repeated PD and Social Order
Last lesson - touch on some intermediate to advanced topics in course of discussing
broader lessons from repeated PD.
Advantages
Lesson 49
Unit 14: Cooperation in the Repeated PD W 8/31
Lesson 49: Repeated PD: General Form
GRIM TRIGGER
Cooperate as long as no-one has defected in the past. If anyone has ever defected,
defect.
Consider a more general form of PD:
2
Defect (Slack Off)
Lesson 48
Lesson 48: Asymmetric Pay-offs in Repeated PD
Another example: Suppose that Row and column have different pay-offs
B
Slack Off
1
A
Slack Off 0
Work Hard
-2
5
6
Work Hard -2
Column is lazier add one to her slacking off pay-offs
3
3
In the previou
Lesson 38
updated 5/28/13
Unit 11: Subgame Perfect Nash Equilibrium
Lesson 38: Sequential Games in Normal Form
Point of Unit 11: Understand subtle difference between Rollback Equilibrium and Nash
Equilibrium
So far: Used Rollback as the method for solving
Lesson 40
Lesson 40: Non-credible Threats and Subgame Perfection
Why didnt we find NE number 2 and 3 via rollback?
Compare definitions
Rollback Equilibrium: Set of strategies, one for each player, in which each player
chooses her best action at each node,
Lesson 35
Lesson 35: Games with PSNE but No MSNE
What if we look for MSNE in games that dont have them?
Well find out well get an answer that doesnt make sense.
example: PD
B
Defect
-2
A
Defect -2
cooperate
-5
0
0
cooperate -5
-1
-1
Look for q = prob (A d
Lesson 24
Lesson 24: Dominant Strategies
Interesting thing about PD is that each player has a dominant strategy: Each does better
by Betray regardless of what the other player does!
So both Betray even though both would do better by Not
Betray
(Defect)
-2
Lesson 29
Lesson 29: Coordination Games
29A Battle of the Sexes
29B Chicken
29C Pure Coordination
Another famous game: Battle of the Sexes
Him
Ballet
1
Her
Ballet 2
Ballgame
0
0
-1
Ballgame -1
2
1
Two NE: One player prefers one, the other players prefers
Lesson 28
Lesson 28: Assurance Game
28A: Non-uniqueness of NE
28B. Multiple equilibria versus multiple cases
Back to apartment cleaning:
Both Clean is a Nash equilibrium.
But so is both Leave Mess.
Punchline: There may be more than one combination of stra
Lesson 27
Unit 8: Nash Equilibrium
Lesson 27: Mutual best response
Left off Unit 7 wondering how to analyze a game in which neither player has a dominant
strategy
Suppose that both players prefer Clean, Clean to I Leave Mess, You Clean
Leave Mess
1
Leave
Unit 9: Mixed Strategies
Lesson 31: No NE?
Cops & Robbers
Robbers
At Work
-5
Cops
On Beat 2
Home
0
1
5
Donuts -5
0
5
1. Notice that there is no NE in pure strategies:
Cops On Beat, Robbers At Work Robbers wish theyd stayed home
Cops On Beat, R Home Cops p
Lesson 32
Lesson 32. Finding MSNE
32A Your EU depends on my probability
32B. You must be indifferent among pure strategies to mix
32C. Equilibrium = My probability makes you indifferent (and vice versa)
Ro
Lesson 45
Unit 13: Indefinitely Repeated PD
Lesson 45. Grim Trigger
45A. Contingent Strategies
45B. NE in Repeated Game
Repeated Interaction
Return to main line of inquiry:
Can the shadow of the future sustain cooperation in repeated PD?
If interaction ha
Lesson 47
Lesson 47: Mutual Grim Trigger as Nash Equilibrium
Need to show not just that GT is better than Unconditional Defect, but better than any
other strategy.
Cannot consider each possible alternative strategy individually - they are infinite
Need to
Zeilberger
1
PS 30 Section 1A
Correction Week 2 (10/6)
Today in class we began with finding the strongly and weakly dominated strategies for the game
below:
First, we found that for both players, the strategy of buying 0 raffle tickets is strongly dominat
B
Midterm PS30 Winter 2016 ANSWER
42 POINTS TOTAL
4 POINTS 1. State the pure strategy Nash equilibrium or equilibria of this matrix:
L
C
R
T
6,6
0,5
3,4
M
3,9
5,1
2,8
B
5,5
4,4
8,7
Pure strategy Nash equilibrium or equilibria:
T,L and B, R
4 POINTS 2. Whi
Exam A
Midterm PS30 Winter 2016 Answers
42 POINTS TOTAL
4 POINTS 1. State the pure strategy Nash equilibrium or equilibria of this matrix:
L
C
R
Pure strategy Nash equilibrium or equilibria:
T
5,5
4,4
8,7
M
3,9
5,1
2,8
B
6,6
0,5
3,4
B,L and T, R
4 POINTS
PS 30
Homework 3
Luke Mostert
Scenario A:
A1)
Leader
Candidate B
Candidate A
(0)
Nature
Star (P)
Dud (1-P)
(2)
(-5)
If the probability that Candidate B is a star is 50% then the optimal decision
would be for the leader to choose Candidate A (as -1.5 < 0)
Political Science 40: Introduction to American Politics
Darin DeWitt
Summer 2015
Examination #2
Print your name: _
Section 1: Multiple Choice (2 points each)
For each multiple choice problem, circle the best answer.
1. The United States Constitution estab
Homework 4 PS 30 October 2016
1. Say that a seller tries to sell a car to a buyer. The car is worth $1000 to the seller and $2000
to the buyer, and both people know this. First, the seller proposes a price of either $1800 or
$1200 to the buyer. Given this
Kaylin Portillo Chavez
Homework 1 PS 30 October 2016
1. This is not a rational choice explanation because within the study it would be based on an unconscious
decision due to empathy. If it were a rational choice explanation then a person would have to ma