Game Theory and Strategy

An exploration of strategic decision-making, covering simultaneous and sequential games, mixed strategies, and applications in matching, voting, and auctions.

This course was a fascinating exploration of the science of strategic decision-making. We began by building a strong foundation in the core types of games, including those with simultaneous and sequential moves, and learned how to analyze them for equilibria. The course then expanded to a wide range of fascinating applications, from evolutionary game theory and the Gale-Shapley matching algorithm to the complexities of social choice and Arrow’s Impossibility Theorem. We also covered cooperative games, fair division problems, auction design, and the strategic implications of network effects, providing a comprehensive view of how to model and understand strategic interactions.

Instructors

Course Schedule & Topics

The course is structured over 12 weeks, moving from fundamental game theory concepts to advanced and applied topics.

Week(s) Primary Focus Key Topics Covered
1 Introduction to Strategic Thinking General principles and foundational concepts of game theory.
2-3 Simultaneous-Move Games Analyzing games where players move at the same time; finding Nash Equilibria.
4 Sequential-Move Games Analyzing games with a defined order of play using game trees and backward induction.
5 Advanced Game Structures Combining sequential and simultaneous moves; introduction to mixed strategies.
6 Evolutionary Game Theory Applying game theory concepts to evolutionary biology and population dynamics.
7 Matching Problems & Algorithms The stable matching problem and the Gale-Shapley algorithm.
8 Social Choice Theory & Voting Analysis of voting systems, information cascades, and Arrow’s Impossibility Theorem.
9 Cooperative Games & Value Introduction to cooperative games and methods for value allocation like Shapley Values.
10 Fair Division Problems Exploring fair division methods and bankruptcy problems.
11 Auction Theory & Design Analysis of different auction types and strategic bidding.
12 Network Effects Understanding the strategic implications of network effects in business and technology.

Material used