Difference between revisions of "BSc: Game Theory"

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= Game Theory =
  
= Game Theory =
  +
* '''Course name''': Game Theory
  +
* '''Code discipline''': R-01
  +
* '''Subject area''':
   
  +
== Short Description ==
−
* <span>'''Course name:'''</span> Game Theory
  
  +
This course covers the following concepts: Game Theory: Basics of the mathematical theory of games, including Nash Equilibrium, Mixed Strategies, and Evolutionary Game Theory; Applications of Computer Programming: Implementation of Game Playing agents.
−
* <span>'''Course number:'''</span> R-01
  
   
−
== Course Characteristics ==
 +
== Prerequisites ==
   
−
=== Key concepts of the class ===
 +
=== Prerequisite subjects ===
  +
* [https://eduwiki.innopolis.university/index.php/BSc:AnalyticGeometryAndLinearAlgebraII CSE204 — Analytic Geometry And Linear Algebra II]: real vector and matrix operations, convex hull and span.
  +
* [https://eduwiki.innopolis.university/index.php/BSc:ProbabilityAndStatistics CSE206 — Probability And Statistics]: probability distribution and mean function.
  +
* [https://eduwiki.innopolis.university/index.php/BSc:MathematicalAnalysisI CSE201 — Mathematical Analysis II]: extreme values of differentiable functions.
  +
* [https://eduwiki.innopolis.university/index.php/BSc:Logic_and_Discrete_Mathematics CSE113 — Philosophy I - (Discrete Math and Logic)]: paths in directed acyclic weighted graphs.
   
  +
=== Prerequisite topics ===
−
* Game Theory: Basics of the mathematical theory of games, including Nash Equilibrium, Mixed Strategies, and Evolutionary Game Theory
  
−
* Applications of Computer Programming: Implementation of Game Playing agents
  
   
−
=== What is the purpose of this course? ===
  
   
  +
== Course Topics ==
  +
{| class="wikitable"
  +
|+ Course Sections and Topics
  +
|-
  +
! Section !! Topics within the section
  +
|-
  +
| Domination and Nash ||
  +
# 2 by 2 classical games (Chicken, Prisoner’s dilemma, Battle of the Sexes, coin flips)
  +
# n by m games and methods of reduction
  +
# Domination and Nash Equilibrium
  +
# Game Tree Roll Out
  +
|-
  +
| Advanced strategics ||
  +
# Multiple player and random player games
  +
# Higher level Strategic planning including - Shelling’s theory of credible threats and promises
  +
# Introduction to Evolutionary Game theory
  +
|-
  +
| Tournament and Agents ||
  +
# Agent players
  +
# Computer Tournaments and Evolutionary Tournaments
  +
|}
  +
== Intended Learning Outcomes (ILOs) ==
  +
  +
=== What is the main purpose of this course? ===
 
Game Theory is a powerful method to make predictive decisions about common business cases and acts as a foundational course to decision making in AI systems, such as Bayesian techniques and game trees and Monte Carlo Tree Search. As such the purpose of this course is to provide a solid foundation on the basic structures of mathematical games including the canonical 2 by 2 structures of the Prisoner’s Dilemma, Chicken, Hawk and Dove, and Battle of the Sexes. Then looks at more complicated business examples such as price setting, making creditable threats and promises. It also gives practical instruction on the application of computers in game playing, especially tournament play and development of decision making models.
  
Game Theory is a powerful method to make predictive decisions about common business cases and acts as a foundational course to decision making in AI systems, such as Bayesian techniques and game trees and Monte Carlo Tree Search. As such the purpose of this course is to provide a solid foundation on the basic structures of mathematical games including the canonical 2 by 2 structures of the Prisoner’s Dilemma, Chicken, Hawk and Dove, and Battle of the Sexes. Then looks at more complicated business examples such as price setting, making creditable threats and promises. It also gives practical instruction on the application of computers in game playing, especially tournament play and development of decision making models.
   
  +
=== ILOs defined at three levels ===
−
== Prerequisites ==
  
−
* [https://eduwiki.innopolis.university/index.php/BSc:AnalyticGeometryAndLinearAlgebraI Analytic Geometry And Linear Algebra I]
  
−
* [https://eduwiki.innopolis.university/index.php/BSc:AnalyticGeometryAndLinearAlgebraII Analytic Geometry And Linear Algebra II]: real vector and matrix operations, convex hull and span.
  
−
* Probability: probability distribution and mean function.
 
−
* Calculus: extreme values of differentiable functions. Discrete Math: paths in directed acyclic weighted graphs.
  
−  
−  
−  
−
=== Course objectives based on Bloom’s taxonomy ===
  
−  
−
=== - What should a student remember at the end of the course? ===
  
−  
−
By the end of the course, the students should be able to give basic definitions of games
  
   
  +
==== Level 1: What concepts should a student know/remember/explain? ====
  +
By the end of the course, the students should be able to ...
 
* Should be able to define Nash Equilibrium, Domination, Mixed v. Pure Strategies
  
* Should be able to define Nash Equilibrium, Domination, Mixed v. Pure Strategies
 
* Should be able to define Evolutionary Stability
  
* Should be able to define Evolutionary Stability
 
* Should be able to define a number of common agent types (always cooperate/defect, Tit-for-tat, Grudger)
  
* Should be able to define a number of common agent types (always cooperate/defect, Tit-for-tat, Grudger)
   
−
=== - What should a student be able to understand at the end of the course? ===
 +
==== Level 2: What basic practical skills should a student be able to perform? ====
  +
By the end of the course, the students should be able to ...
−  
−
By the end of the course, the students should be able to understand the basic
  
−  
 
* A student should understand how game theory affects common daily situations, such as internet trade (as a PD)
  
* A student should understand how game theory affects common daily situations, such as internet trade (as a PD)
 
* Should understand the role of Evolutionary Stable Strategies
  
* Should understand the role of Evolutionary Stable Strategies
 
* Should understand the history of tournaments as methods to evaluate agent play
  
* Should understand the history of tournaments as methods to evaluate agent play
   
−
=== - What should a student be able to apply at the end of the course? ===
 +
==== Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios? ====
  +
By the end of the course, the students should be able to ...
−  
−
By the end of the course, the students should be able to apply game theory to solve problems in limited real world cases.
  
−  
 
* Program a finite state machine to play iterated games
  
* Program a finite state machine to play iterated games
 
* Apply both domination and Nash equilibrium to solve pure games
  
* Apply both domination and Nash equilibrium to solve pure games
−
* Apply both domination, Nash equilibrium, and mixed strategies to solve mixed strategic games
 +
* Apply both domination, Nash equilibrium, and mixed strategies to solve mixed strategic games
  +
== Grading ==
   
−
=== Course evaluation ===
 +
=== Course grading range ===
  +
{| class="wikitable"
−  
−
{|
 +
|+
−
|+ Course grade breakdown
  
−
!
  
−
!
  
−
!align="center"| '''Proposed points'''
  
 
|-
  
|-
  +
! Grade !! Range !! Description of performance
−
| Labs/seminar classes
  
−
| 10
  
−
|align="center"|
  
 
|-
  
|-
  +
| A. Excellent || 90-100 || -
−
| Interim performance assessment
  
−
| 40
  
−
|align="center"|
  
 
|-
  
|-
  +
| B. Good || 75-89 || -
−
| Midterm and Exam
  
−
| 50
 +
|-
  +
| C. Satisfactory || 60-74 || -
−
|align="center"|
  
  +
|-
  +
| D. Poor || 0-59 || -
 
|}
  
|}
   
  +
=== Course activities and grading breakdown ===
−
If necessary, please indicate freely your course’s features in terms of students’ performance assessment.
  
  +
{| class="wikitable"
−  
  +
|+
−
=== Grades range ===
  
−  
−
{|
  
−
|+ Course grading range
  
−
!
  
−
!
  
−
!align="center"| '''Proposed range'''
  
 
|-
  
|-
  +
! Activity Type !! Percentage of the overall course grade
−
| A. Excellent
  
−
| 90-100
  
−
|align="center"|
  
 
|-
  
|-
  +
| Labs/seminar classes || 10
−
| B. Good
  
−
| 75-89
  
−
|align="center"|
  
 
|-
  
|-
  +
| Interim performance assessment || 40
−
| C. Satisfactory
  
−
| 60-74
  
−
|align="center"|
  
 
|-
  
|-
  +
| Midterm and Exam || 50
−
| D. Poor
  
−
| 0-59
  
−
|align="center"|
  
 
|}
  
|}
   
  +
=== Recommendations for students on how to succeed in the course ===
−
This course has a required class element of practical work on course elements, the retake is not a substitute for practical knowledge, and it is inherently unfair that students who have not submitted these practical elements are graded the same as those who have accomplished course materials. In order to be eligible for the retake, a student is required to have submitted all course assignments, and have a passing grade on those elements. The lacking/failing elements, can be presented for this purpose up to 3 business days before the retake for evaluation. In the case of the resubmission of a failing element, a document should be attached noting which changes have been made to the assignment in order to lead to a passing mark. Lack of these elements in a passing state presented to the committee will be considered a failing grade for the retake.
  
   
−
The retake grade will count as the final course grade, with the first retake giving no more than a B as final grade, and the second retake giving no more than a C. The first retake will be a written exam submitted to the professor, and the second retake as an oral commission.
  
   
−
=== Resources and reference material ===
 +
== Resources, literature and reference materials ==
   
  +
=== Open access resources ===
−
* Andrew McEachern, Game Theory : A Classical Introduction, Mathematical Games, and the Tournament
  
  +
* Andrew McEachern, Game Theory : A Classical Introduction, Mathematical Games, and the Tournament
 
* Thomas Schelling, Strategy and Conflict
  
* Thomas Schelling, Strategy and Conflict
 
* William Poundstone, Prisoner’s Dilemma
  
* William Poundstone, Prisoner’s Dilemma
   
−
== Course Sections ==
 +
=== Closed access resources ===
   
−
The main sections of the course and approximate hour distribution between them is as follows:
  
   
  +
=== Software and tools used within the course ===
−
{|
  
  +
−
|+ Course Sections
  
  +
= Teaching Methodology: Methods, techniques, & activities =
−
!align="center"| '''Section'''
  
  +
−
! '''Section Title'''
  
−
!align="center"| '''Teaching Hours'''
 +
== Activities and Teaching Methods ==
  +
{| class="wikitable"
  +
|+ Activities within each section
 
|-
  
|-
  +
! Learning Activities !! Section 1 !! Section 2 !! Section 3
−
|align="center"| 1
  
−
| Domination and Nash
  
−
|align="center"| 16
  
 
|-
  
|-
  +
| Homework and group projects || 1 || 1 || 1
−
|align="center"| 2
  
−
| Advanced strategics
  
−
|align="center"| 16
  
 
|-
  
|-
  +
| Midterm evaluation || 1 || 0 || 0
−
|align="center"| 3
  
  +
|-
−
| Tournament and Agents
  
  +
| Testing (written or computer based) || 1 || 1 || 1
−
|align="center"| 16
  
−
|}
 +
|-
  +
| Oral polls || 1 || 0 || 1
  +
|-
  +
| Discussions || 1 || 1 || 1
  +
|-
  +
| Development of individual parts of software product code || 0 || 1 || 1
  +
|-
  +
| Reports || 0 || 0 || 1
  +
|}
  +
== Formative Assessment and Course Activities ==
   
−
=== Section 1 ===
 +
=== Ongoing performance assessment ===
−  
−
==== Section title: ====
  
−  
−
Domination and Nash
  
−  
−
=== Topics covered in this section: ===
  
−  
−
* 2 by 2 classical games (Chicken, Prisoner’s dilemma, Battle of the Sexes, coin flips)
  
−
* n by m games and methods of reduction
  
−
* Domination and Nash Equilibrium
  
−
* Game Tree Roll Out
  
−  
−
=== What forms of evaluation were used to test students’ performance in this section? ===
  
−  
−
<div class="tabular">
  
−  
−
<span>|a|c|</span> &amp; '''Yes/No'''<br />
  
−
Development of individual parts of software product code &amp; 0<br />
  
−
Homework and group projects &amp; 1<br />
  
−
Midterm evaluation &amp; 1<br />
  
−
Testing (written or computer based) &amp; 1<br />
  
−
Reports &amp; 0<br />
  
−
Essays &amp; 0<br />
  
−
Oral polls &amp; 1<br />
  
−
Discussions &amp; 1<br />
  
−  
−  
−  
−
</div>
  
−
=== Typical questions for ongoing performance evaluation within this section ===
  
−  
−
# What is an externality in PD?
  
−
# Give the Nash Equilibrium of an example 2 by 2 game
  
−
# Give the Domination in an example n by m game
  
−
# What is the payoff matrix for a given game
  
−  
−
=== Typical questions for seminar classes (labs) within this section ===
  
−  
−
# List and example the set of externalities of PD
  
−
# Worked examples of Nash Equlibrium
  
−
# Worked examples of Domination
  
−
# Given the payoff matrix for a given game, what is the outcome of play.
  
−  
−
=== Test questions for final assessment in this section ===
  
   
  +
==== Section 1 ====
  +
{| class="wikitable"
  +
|+
  +
|-
  +
! Activity Type !! Content !! Is Graded?
  +
|-
  +
| Question || What is an externality in PD? || 1
  +
|-
  +
| Question || Give the Nash Equilibrium of an example 2 by 2 game || 1
  +
|-
  +
| Question || Give the Domination in an example n by m game || 1
  +
|-
  +
| Question || What is the payoff matrix for a given game || 1
  +
|-
  +
| Question || List and example the set of externalities of PD || 0
  +
|-
  +
| Question || Worked examples of Nash Equlibrium || 0
  +
|-
  +
| Question || Worked examples of Domination || 0
  +
|-
  +
| Question || Given the payoff matrix for a given game, what is the outcome of play. || 0
  +
|}
  +
==== Section 2 ====
  +
{| class="wikitable"
  +
|+
  +
|-
  +
! Activity Type !! Content !! Is Graded?
  +
|-
  +
| Question || Using Domination and Nash Equilibrium find a mixed strategy solution for a given game. || 1
  +
|-
  +
| Question || How does this game differ if we only allow for pure strategies rather than mixed? || 1
  +
|-
  +
| Question || What is the difference between Evolutionary Stable Strategies and Dominator Theory || 1
  +
|-
  +
| Question || What is the ESS for an Iterated Prisoner’s Dilemma? || 1
  +
|-
  +
| Question || Why does IPD not have a clear Nash Equilibrium and why should we use a Evolutionary Stable Strategies || 0
  +
|-
  +
| Question || Show the finite state representation for TFT || 0
  +
|-
  +
| Question || Demonstrate the Outcome of a population of half ALLC and half ALLD || 0
  +
|-
  +
| Question || Demonstrate the Best Response method on an example matrix || 0
  +
|}
  +
==== Section 3 ====
  +
{| class="wikitable"
  +
|+
  +
|-
  +
! Activity Type !! Content !! Is Graded?
  +
|-
  +
| Question || Define the meaning of a lock box. || 1
  +
|-
  +
| Question || Define the meaning of a nice strategy. || 1
  +
|-
  +
| Question || How can we make a strategy more cooperative by changing its structure? || 1
  +
|-
  +
| Question || Give a listing of IPD agents and a short description of their ruleset || 1
  +
|-
  +
| Question || Program a finite state machine for IPD which implements a Lock Box || 0
  +
|-
  +
| Question || What properties does a finite state machine have (i.e. is it nice) || 0
  +
|-
  +
| Question || If a state machine is nice - what does it’s transitions matrix look like? || 0
  +
|-
  +
| Question || How can a 3 and 4 state lockbox reach cooperation? || 0
  +
|}
  +
=== Final assessment ===
  +
'''Section 1'''
 
# List and example the set of externalities of PD
  
# List and example the set of externalities of PD
 
# Worked examples of Nash Equilibrium and Domination
  
# Worked examples of Nash Equilibrium and Domination
 
# Given the payoff matrix for a given game, what is the outcome of play.
  
# Given the payoff matrix for a given game, what is the outcome of play.
 
# A button is put before you. If you don’t press the button you get a low passing grade on this question. If you press the button and less than half the class presses the button you get a high passing grade for this question. If more than half the class presses the button then those who press the button get a failing grade for this question. Do you press the button?
  
# A button is put before you. If you don’t press the button you get a low passing grade on this question. If you press the button and less than half the class presses the button you get a high passing grade for this question. If more than half the class presses the button then those who press the button get a failing grade for this question. Do you press the button?
  +
'''Section 2'''
−  
−
=== Section 2 ===
  
−  
−
==== Section title: ====
  
−  
−
Advanced strategics
  
−  
−
=== Topics covered in this section: ===
  
−  
−
* Multiple player and random player games
  
−
* Higher level Strategic planning including - Shelling’s theory of credible threats and promises
  
−
* Introduction to Evolutionary Game theory
  
−  
−
=== What forms of evaluation were used to test students’ performance in this section? ===
  
−  
−
<div class="tabular">
  
−  
−
<span>|a|c|</span> &amp; '''Yes/No'''<br />
  
−
Development of individual parts of software product code &amp; 1<br />
  
−
Homework and group projects &amp; 1<br />
  
−
Midterm evaluation &amp; 0<br />
  
−
Testing (written or computer based) &amp; 1<br />
  
−
Reports &amp; 0<br />
  
−
Essays &amp; 0<br />
  
−
Oral polls &amp; 0<br />
  
−
Discussions &amp; 1<br />
  
−  
−  
−  
−
</div>
  
−
=== Typical questions for ongoing performance evaluation within this section ===
  
−  
−
# Using Domination and Nash Equilibrium find a mixed strategy solution for a given game.
  
−
# How does this game differ if we only allow for pure strategies rather than mixed?
  
−
# What is the difference between Evolutionary Stable Strategies and Dominator Theory
  
−
# What is the ESS for an Iterated Prisoner’s Dilemma?
  
−  
−
=== Typical questions for seminar classes (labs) within this section ===
  
−  
−
# Why does IPD not have a clear Nash Equilibrium and why should we use a Evolutionary Stable Strategies
  
−
# Show the finite state representation for TFT
  
−
# Demonstrate the Outcome of a population of half ALLC and half ALLD
  
−
# Demonstrate the Best Response method on an example matrix
  
−  
−
=== Test questions for final assessment in this section ===
  
−  
 
# Simulate the IPD, does the ESS occur?
  
# Simulate the IPD, does the ESS occur?
 
# When the time-line of an ESS is extended but we include the restriction of a finite space, what happens to the equilibriumum
  
# When the time-line of an ESS is extended but we include the restriction of a finite space, what happens to the equilibriumum
 
# Demonstrate the Best Response method on an example matrix
  
# Demonstrate the Best Response method on an example matrix
  +
'''Section 3'''
  +
# Show a working finite state machine IPD model of Trifecta.
  +
# Create a Tournament agent to compete against your classmates for a given game.
  +
# Given a set of players for a IPD model, what is the most likely equilibrium outcome, explain.
   
−
=== Section 3 ===
 +
=== The retake exam ===
  +
'''Section 1'''
   
−
==== Section title: ====
 +
'''Section 2'''
   
  +
'''Section 3'''
−
Tournament and Agents
  
−  
−
==== Topics covered in this section: ====
  
−  
−
* Agent players
  
−
* Computer Tournaments and Evolutionary Tournaments
  
−  
−
=== What forms of evaluation were used to test students’ performance in this section? ===
  
−  
−
<div class="tabular">
  
−  
−
<span>|a|c|</span> &amp; '''Yes/No'''<br />
  
−
Development of individual parts of software product code &amp; 1<br />
  
−
Homework and group projects &amp; 1<br />
  
−
Midterm evaluation &amp; 0<br />
  
−
Testing (written or computer based) &amp; 1<br />
  
−
Reports &amp; 1<br />
  
−
Essays &amp; 0<br />
  
−
Oral polls &amp; 1<br />
  
−
Discussions &amp; 1<br />
  
−  
−  
−  
−
</div>
  
−
=== Typical questions for ongoing performance evaluation within this section ===
  
−  
−
# Define the meaning of a lock box.
  
−
# Define the meaning of a nice strategy.
  
−
# How can we make a strategy more cooperative by changing its structure?
  
−
# Give a listing of IPD agents and a short description of their ruleset
  
−  
−
==== Typical questions for seminar classes (labs) within this section ====
  
−  
−
# Program a finite state machine for IPD which implements a Lock Box
  
−
# What properties does a finite state machine have (i.e. is it nice)
  
−
# If a state machine is nice - what does it’s transitions matrix look like?
  
−
# How can a 3 and 4 state lockbox reach cooperation?
  
−  
−
==== Test questions for final assessment in this section ====
  
−  
−
# Show a working finite state machine IPD model of Trifecta.
  
−
# Create a Tournament agent to compete against your classmates for a given game.
  
−
# Given a set of players for a IPD model, what is the most likely equilibrium outcome, explain.
  

Latest revision as of 11:02, 13 July 2022

Game Theory

  • Course name: Game Theory
  • Code discipline: R-01
  • Subject area:

Short Description

This course covers the following concepts: Game Theory: Basics of the mathematical theory of games, including Nash Equilibrium, Mixed Strategies, and Evolutionary Game Theory; Applications of Computer Programming: Implementation of Game Playing agents.

Prerequisites

Prerequisite subjects

Prerequisite topics

Course Topics

Course Sections and Topics
Section Topics within the section
Domination and Nash
  1. 2 by 2 classical games (Chicken, Prisoner’s dilemma, Battle of the Sexes, coin flips)
  2. n by m games and methods of reduction
  3. Domination and Nash Equilibrium
  4. Game Tree Roll Out
Advanced strategics
  1. Multiple player and random player games
  2. Higher level Strategic planning including - Shelling’s theory of credible threats and promises
  3. Introduction to Evolutionary Game theory
Tournament and Agents
  1. Agent players
  2. Computer Tournaments and Evolutionary Tournaments

Intended Learning Outcomes (ILOs)

What is the main purpose of this course?

Game Theory is a powerful method to make predictive decisions about common business cases and acts as a foundational course to decision making in AI systems, such as Bayesian techniques and game trees and Monte Carlo Tree Search. As such the purpose of this course is to provide a solid foundation on the basic structures of mathematical games including the canonical 2 by 2 structures of the Prisoner’s Dilemma, Chicken, Hawk and Dove, and Battle of the Sexes. Then looks at more complicated business examples such as price setting, making creditable threats and promises. It also gives practical instruction on the application of computers in game playing, especially tournament play and development of decision making models.

ILOs defined at three levels

Level 1: What concepts should a student know/remember/explain?

By the end of the course, the students should be able to ...

  • Should be able to define Nash Equilibrium, Domination, Mixed v. Pure Strategies
  • Should be able to define Evolutionary Stability
  • Should be able to define a number of common agent types (always cooperate/defect, Tit-for-tat, Grudger)

Level 2: What basic practical skills should a student be able to perform?

By the end of the course, the students should be able to ...

  • A student should understand how game theory affects common daily situations, such as internet trade (as a PD)
  • Should understand the role of Evolutionary Stable Strategies
  • Should understand the history of tournaments as methods to evaluate agent play

Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?

By the end of the course, the students should be able to ...

  • Program a finite state machine to play iterated games
  • Apply both domination and Nash equilibrium to solve pure games
  • Apply both domination, Nash equilibrium, and mixed strategies to solve mixed strategic games

Grading

Course grading range

Grade Range Description of performance
A. Excellent 90-100 -
B. Good 75-89 -
C. Satisfactory 60-74 -
D. Poor 0-59 -

Course activities and grading breakdown

Activity Type Percentage of the overall course grade
Labs/seminar classes 10
Interim performance assessment 40
Midterm and Exam 50

Recommendations for students on how to succeed in the course

Resources, literature and reference materials

Open access resources

  • Andrew McEachern, Game Theory : A Classical Introduction, Mathematical Games, and the Tournament
  • Thomas Schelling, Strategy and Conflict
  • William Poundstone, Prisoner’s Dilemma

Closed access resources

Software and tools used within the course

Teaching Methodology: Methods, techniques, & activities

Activities and Teaching Methods

Activities within each section
Learning Activities Section 1 Section 2 Section 3
Homework and group projects 1 1 1
Midterm evaluation 1 0 0
Testing (written or computer based) 1 1 1
Oral polls 1 0 1
Discussions 1 1 1
Development of individual parts of software product code 0 1 1
Reports 0 0 1

Formative Assessment and Course Activities

Ongoing performance assessment

Section 1

Activity Type Content Is Graded?
Question What is an externality in PD? 1
Question Give the Nash Equilibrium of an example 2 by 2 game 1
Question Give the Domination in an example n by m game 1
Question What is the payoff matrix for a given game 1
Question List and example the set of externalities of PD 0
Question Worked examples of Nash Equlibrium 0
Question Worked examples of Domination 0
Question Given the payoff matrix for a given game, what is the outcome of play. 0

Section 2

Activity Type Content Is Graded?
Question Using Domination and Nash Equilibrium find a mixed strategy solution for a given game. 1
Question How does this game differ if we only allow for pure strategies rather than mixed? 1
Question What is the difference between Evolutionary Stable Strategies and Dominator Theory 1
Question What is the ESS for an Iterated Prisoner’s Dilemma? 1
Question Why does IPD not have a clear Nash Equilibrium and why should we use a Evolutionary Stable Strategies 0
Question Show the finite state representation for TFT 0
Question Demonstrate the Outcome of a population of half ALLC and half ALLD 0
Question Demonstrate the Best Response method on an example matrix 0

Section 3

Activity Type Content Is Graded?
Question Define the meaning of a lock box. 1
Question Define the meaning of a nice strategy. 1
Question How can we make a strategy more cooperative by changing its structure? 1
Question Give a listing of IPD agents and a short description of their ruleset 1
Question Program a finite state machine for IPD which implements a Lock Box 0
Question What properties does a finite state machine have (i.e. is it nice) 0
Question If a state machine is nice - what does it’s transitions matrix look like? 0
Question How can a 3 and 4 state lockbox reach cooperation? 0

Final assessment

Section 1

  1. List and example the set of externalities of PD
  2. Worked examples of Nash Equilibrium and Domination
  3. Given the payoff matrix for a given game, what is the outcome of play.
  4. A button is put before you. If you don’t press the button you get a low passing grade on this question. If you press the button and less than half the class presses the button you get a high passing grade for this question. If more than half the class presses the button then those who press the button get a failing grade for this question. Do you press the button?

Section 2

  1. Simulate the IPD, does the ESS occur?
  2. When the time-line of an ESS is extended but we include the restriction of a finite space, what happens to the equilibriumum
  3. Demonstrate the Best Response method on an example matrix

Section 3

  1. Show a working finite state machine IPD model of Trifecta.
  2. Create a Tournament agent to compete against your classmates for a given game.
  3. Given a set of players for a IPD model, what is the most likely equilibrium outcome, explain.

The retake exam

Section 1

Section 2

Section 3

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