Mathematics of Games (And as a Game!)

Welcome to Students

What can I get out of this course?
In this course you'll learn the basics of game theory and strategic thinking, as a refreshing change of scenery from the traditional math sequence and its emphasis on algebraic computation. We'll learn to recognize that mathematical thinking arises as a refinement of the basic cognitive heuristics that we all use when making decisions in everyday life's interactive contexts.
How is the course structured?
Three strands of investigation set the framework within which various games can be analyzed. We'll talk about (i) individual puzzles pitting the ``player'' against the impartial laws of logic, (ii) competitive games pitting the player against one rational opponent, and (iii) probabilistic games pitting players against ``controlled randomness'', where informed strategy decisions can help turn the odds to their favor.
What books do I need to purchase?
The first two books listed below will be discussed as a class, so you have to obtain a personal copy. Other texts are listed here in case you want further references or ideas for individual research projects.
  • Fisher, Len. Rock, Paper, Scissors: Game Theory in Everyday Life
  • Lewis, Michael. Moneyball
  • Davis, Morton. Game Theory: A Nontechnical Introduction
  • Dixit, Avinash. Thinking Strategically: The Competitive Edge in Business, Politics, and Everyday Life
  • Gintis, Herbert. Game Theory Evolving
What skills should I focus on as the semester proceeds?
By the end of the course you should be able to:
  1. Determine the optimal strategy for simple competitive games
  2. Analyze social issues within the framework of game theory
  3. Construct decision trees
  4. Compute expected values
  5. Approach new mathematics problems without anxiety

Notes and Assignments

Overview of Set Theory and Probability
(adapted from Game Theory Evolving)
Week 2 Journal:
Rock, Paper, Scissors – 2x2 Games
Week 3 Journal:
Rock, Paper, Scissors – Fair Division
Week 4 Journal:
Rock, Paper, Scissors and Pay It Forward – Negotiation
Week 5 Journal:
Rock, Paper, Scissors – Cooperating and Gaining Trust
Midterm Project:
Game Theory Presentation
Week 9 Journal:
Moneyball Chapter 2
Data Analysis Project
(inspired by Moneyball)
Week 11 Journal:
Moneyball Chapters 4 and 5
Week 12 Journal:
Moneyball Chapter 7
Week 13 Journal:
Moneyball Chapters 8 and 9
Week 14 Journal:
Moneyball Chapters 10 and 11
Week 15 Journal:
Moneyball Chapter 12, Epilogue, and Afterword