• Home
  • YouTube Channel
    • All Playlists on YouTube
  • TI-84 Tutorials
  • How to Convert HW to a PDF File
  • Graph Paper
  • M104 at IUK
    • TI-84 Tutorials
    • MyMathLab Registration
    • Semester Schedule
    • Chapter 1
    • Chapter 2
    • Chapter 3
    • Chapter 4
    • Chapter 5
    • Practice Tests
    • Released Exams & Quizzes
  • M105 at IUK
    • TI-84 Tutorials
    • Semester Schedule & M105 At A Glance
    • Course Syllabus & Lecture Content List
    • Chapter 5
    • Chapter 6
    • Chapter 7
    • Chapter 4
    • Chapter 8
    • Test Review
    • Released Exams & Quizzes
  • AP Calculus AB at THS
    • Calculus Class Pictures
    • Calculus Student Inventory
    • TI-84 Tutorials
    • Zoom Meeting Recordings
    • Monthly Calendars
    • Web Assignments
    • AP College Board YouTube
    • AP Calculus AB Exam
    • ACP Calculus - IU
    • Memorization Sheets
    • Calculus Memorization Quizzes
    • Test/Quiz Correction Analysis
    • Chapter P
    • Chapter 1
    • Chapter 2
    • Chapter 3
    • Chapter 4
    • Chapter 5
    • Chapter 6
    • Chapter 7
    • Chapter 8
    • Last Chapter/Review
    • Final Exam Review WS
    • The Calculus Life Saver
    • Final Calculus Video Project
    • Past AP Calculus AB Scores
  • Pre-Calculus (H) at THS
    • TI-84 Tutorials
    • Monthly Calendars
    • Pre-Calculus Student Inventory
    • Trig Memorization Quizzes
    • Web Logs >
      • Web Log #1
      • Web Log #2
      • Web Log #3
      • Web Log #4
      • Web Log #5
      • Web Log #6
      • Web Log #7
      • Web Log #8
      • Web Log #9
      • Web Log #10
      • Web Log #11
      • Web Logs #12 - 17
    • Chapter 1
    • Chapter 2
    • Chapter 3
    • Chapter 4
    • Chapter 5
    • Chapter 6
    • Chapter 8
    • Chapter 7
    • Final Exam Study Guides
    • Regression Project
    • Are You Ready for Calculus? >
      • Independent Calculus Preparation
      • ETSU Calculus I Readiness Assessment
      • University of California Calculus Readiness Test
      • Sample Mathematics Placement Exam
      • Paper & Pencil Practice Exams
  • Pre-Calculus (R) at THS
    • TI-84 Tutorials
    • Pre-Calculus Student Inventory
    • Monthly Calendars
    • Zoom Meeting Recordings
    • Chapter P
    • Chapter 1
    • Chapter 2
    • Chapter 3
    • Chapter 4
    • Chapter 5
    • Chapter 6
    • Chapter 7
    • Chapter 10
    • Projects >
      • Math Goes To The Movies
      • Curve Project Screencast
      • Topic Screencast
      • Let The Artist in You Shine! Project
      • Mathematician Presentation Using Google Slides
      • Which Mathematician Was Born on Your Birthday? Project
      • Parabola Project Using Desmos
      • Regression Project
      • Programming the TI-84 Project
      • Law of Sines & Law of Cosines Diorama Project
      • Trigonometry Goes To The Movies A Poster Project
  • Exit Ticket
  • Calculator Recommendation
  • Cole's World of Mathematics Disclaimer
    • Cole's World of Mathematics Privacy Policy
COLE'S WORLD OF MATHEMATICS
  • Home
  • YouTube Channel
    • All Playlists on YouTube
  • TI-84 Tutorials
  • How to Convert HW to a PDF File
  • Graph Paper
  • M104 at IUK
    • TI-84 Tutorials
    • MyMathLab Registration
    • Semester Schedule
    • Chapter 1
    • Chapter 2
    • Chapter 3
    • Chapter 4
    • Chapter 5
    • Practice Tests
    • Released Exams & Quizzes
  • M105 at IUK
    • TI-84 Tutorials
    • Semester Schedule & M105 At A Glance
    • Course Syllabus & Lecture Content List
    • Chapter 5
    • Chapter 6
    • Chapter 7
    • Chapter 4
    • Chapter 8
    • Test Review
    • Released Exams & Quizzes
  • AP Calculus AB at THS
    • Calculus Class Pictures
    • Calculus Student Inventory
    • TI-84 Tutorials
    • Zoom Meeting Recordings
    • Monthly Calendars
    • Web Assignments
    • AP College Board YouTube
    • AP Calculus AB Exam
    • ACP Calculus - IU
    • Memorization Sheets
    • Calculus Memorization Quizzes
    • Test/Quiz Correction Analysis
    • Chapter P
    • Chapter 1
    • Chapter 2
    • Chapter 3
    • Chapter 4
    • Chapter 5
    • Chapter 6
    • Chapter 7
    • Chapter 8
    • Last Chapter/Review
    • Final Exam Review WS
    • The Calculus Life Saver
    • Final Calculus Video Project
    • Past AP Calculus AB Scores
  • Pre-Calculus (H) at THS
    • TI-84 Tutorials
    • Monthly Calendars
    • Pre-Calculus Student Inventory
    • Trig Memorization Quizzes
    • Web Logs >
      • Web Log #1
      • Web Log #2
      • Web Log #3
      • Web Log #4
      • Web Log #5
      • Web Log #6
      • Web Log #7
      • Web Log #8
      • Web Log #9
      • Web Log #10
      • Web Log #11
      • Web Logs #12 - 17
    • Chapter 1
    • Chapter 2
    • Chapter 3
    • Chapter 4
    • Chapter 5
    • Chapter 6
    • Chapter 8
    • Chapter 7
    • Final Exam Study Guides
    • Regression Project
    • Are You Ready for Calculus? >
      • Independent Calculus Preparation
      • ETSU Calculus I Readiness Assessment
      • University of California Calculus Readiness Test
      • Sample Mathematics Placement Exam
      • Paper & Pencil Practice Exams
  • Pre-Calculus (R) at THS
    • TI-84 Tutorials
    • Pre-Calculus Student Inventory
    • Monthly Calendars
    • Zoom Meeting Recordings
    • Chapter P
    • Chapter 1
    • Chapter 2
    • Chapter 3
    • Chapter 4
    • Chapter 5
    • Chapter 6
    • Chapter 7
    • Chapter 10
    • Projects >
      • Math Goes To The Movies
      • Curve Project Screencast
      • Topic Screencast
      • Let The Artist in You Shine! Project
      • Mathematician Presentation Using Google Slides
      • Which Mathematician Was Born on Your Birthday? Project
      • Parabola Project Using Desmos
      • Regression Project
      • Programming the TI-84 Project
      • Law of Sines & Law of Cosines Diorama Project
      • Trigonometry Goes To The Movies A Poster Project
  • Exit Ticket
  • Calculator Recommendation
  • Cole's World of Mathematics Disclaimer
    • Cole's World of Mathematics Privacy Policy
COLE'S WORLD OF MATHEMATICS
Game Theory Unit
Game Theory is the study of mathematical models of strategic interaction between rational decision-makers.  It has applications in all fields of social science, as well as in logic and computer science.  

Originally, it addressed zero-sum games, in which one person's gains result in losses for the other participants. Today, Game Theory applies to a wide range of behavioral relations, and is now an umbrella term for the science of logical decision making in humans, animals, and computers.

Picture
Emile Borel (1871 - 1956)
Emile Borel: The Forgotten Father of Game Theory?
In 1921, Emile Borel, a French mathematician, published several papers on the theory of games.  He used poker as an example and looked at the problem of bluffing and second-guessing the opponent.  Borel envisioned game theory as being use in economic and military applications.  While Borel could be arguably be known as the first mathematician to envision an organized system for playing games, he did not develop his ideas very far.  For that reason, most historians give the credit for developing and popularizing game theory to John Von Neumann, who published his first paper on game theory in 1928, seven year after Borel.
Picture
John Van Neumann (1903 - 1957)

Lecture Notes & Other Resources
Game Theory - Day 1
Explaining a Cornerstone of Game Theory: John Nash's Equilibrium Theory

-----MOVIE CLIP: A Beautiful Mind
This is the scene in the movie where John Nash comes up with the idea for the Nash Equilibrium. However, the scene does not depict the Nash Equilibrium at all, but instead, shows Nash using backward induction.

-----VIDEO CLIP: The Prisoner's Dilemma
This is an example of the Nash Equilibrium.
Picture
John Nash (1928 - 2015)

Game Theory - Day 2
Probability and Game Theory in The Hunger Games

Game Theory - Day 3
Various Board Games

-----PDF: The Game Theory of Othello (Reversi)

-----VIDEO: Understanding the Mathematics Behind Connect 4

-----VIDEO: How To Always Win At Dots and Boxes

-----VIDEO: How To Play Koane (Hawaiian Checkers)

Game Theory - Day 4
Variations of Tic-Tac-Toe

-----VIDEO: Tic Tac Toe - X's Only

-----VIDEO: Secrets of 3-Board Tic-Tac-Toe

Picture
Copyright © 2013-21
​Cole's World of Mathematics.
ALL RIGHTS RESERVED.
Picture
Picture