# Complexity Explorer Santa Few Institute

## Game Theory I • Static Games

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Game theory is the standard quantitative tool for analyzing the interactions of multiple decision makers. Its applications extend to economics, biology, engineering and even cyber security. Furthermore, many complex systems involve multiple decision makers and thus a full analysis of such systems necessitates the tools of game theory. This course is designed to provide a high-level introduction to static, non-cooperative game theory. The main goal of this course is to introduce students to the idea of a Nash Equilibrium and how the Nash Equilibrium solution concept can be applied to a number of scenarios. Students are assumed to be familiar with the concept of expected value and the basics of probability. While calculus is not required for the majority of the course, lesson 7 focuses on an example that employs calculus. However, lesson 7 can be skipped without any harm in understanding lessons 8 − 10.

Justin Grana is a postdoctoral fellow at the Santa Fe Institute. He earned a Ph.D. in economics from American University in 2016 and his research focuses on how the timing of events and decisions impacts interacting humans. To apply his research, Justin has analyzed computer network attacks, collusive cartel formation and air traffic control scenarios.

How to use Complexity Explorer
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3,082

Prerequisites:

Basic Probability

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### Syllabus

1. What is Game Theory?
2. Elements of a Game and the Normal Form Representation
3. Nash Equilibrium
4. Two Examples - Dominant Strategies and Coordination Games
5. Mixed Strategy Nash Equilibrium
6. Brief Historical Interlude
7. A Calculus-Based Example
8. Bayesian Games: Introducing Uncertainty
9. Example: Cyber Security
10. Example: Tragedy of the Commons
11. Summary