BSc: Game Theory

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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