Probability and Game Theory
- Grades 7-11
- Advanced CTY-Level
The study of probability and game theory allows students to apply math to real-world situations. In this course, you’ll learn to use some of the major tools of game theory, a branch of mathematics focused on the application of mathematical reasoning to competitive behavior. You’ll explore concepts like dominance, mixed strategies, utility theory, Nash equilibria, and n-person games, and learn how to use tools from probability and linear algebra to analyze and develop successful game strategies. The games you’ll “play” in this course are abstract representations of real-life situations; for example, Nash equilibria have been used to solve questions of political competition and analyze penalty kicks in soccer, and the Prisoner’s Dilemma has been used to examine the social networks of different populations. Class exercises involve individual and group work and may also include fun class tournaments.
Typical Class Size: 16-18
- Review and apply the fundamentals of probability to solve mathematical problems and develop an understanding of the theoretical foundations for fundamental models in game theory
- Apply fundamentals of probability, linear algebra, and game theory to model certain types of human behavior in competitive decision-making situations
- Determine and use appropriate solution techniques for models of competitive decision-making problems by playing games, and justify solutions
- Examine and apply concepts including mixed strategies, zero-sum games, Nash equilibria, subgame perfect equilibria, Bayesian games, signaling games, and cooperative games
- Utilize real-life and computer simulations to test theories and justify conclusions
- Share ideas and solutions to problems, both written and orally through individual exercises and collaborative projects or tournaments
Summer Dates & Locations
Testing and Prerequisites
|Required Level||Advanced CTY-Level||Not required|
Students must achieve qualifying scores on an advanced assessment to be eligible for CTY programs. If you don’t have qualifying scores, you have several different testing options. We’ll help you find the right option for your situation.Sign up for Testing Learn More
Course PrerequisitesProbability and Game Theory requires:
Cost and Financial Aid
- Nonrefundable Application Fee - $50 (Waived for financial aid applicants)
- Nonrefundable International Fee - $250 (outside US only)
Financial Aid is available
We are committed to serving all talented youth regardless of financial circumstances. Financial assistance is available based on need.
Please acquire all course materials by the course start date, unless noted as perishable. Items marked as “perishable” should not be acquired until the student needs them in the course. If you have questions about these materials or difficulty locating them, please contact [email protected].
These titles have been featured in past sessions of the course, and may be included this summer. CTY provides students with all texts; no purchase is required.
- Game Theory and Strategy, Philip D. Straffin
- Thinking Strategically, Avinash K. Dixit and Barry J. Nalebuff
About Mathematics at CTY
Explore the study of shapes
Many of our courses allow students to describe the world around them in basic and profound ways. Our younger students learn about shape, scale, and proportion in Geometry and Spatial Sense. Middle School students explore beautiful real-world applications of lines; analyze data based on curves that fit a uniform, symmetric and bell-shaped, or skewed pattern in Data and Chance. And advanced students explore the underlying mathematics and fundamental characteristics of shapes, distance, and continuous deformations in our proof-based Topology course.
Dive deep into logic and reasoning
Our courses in formal logic give you the tools to question the world around you. Inductive and Deductive Reasoning introduces younger students to different types of reasoning, as well as the strengths and weaknesses inherent in various forms of critical analysis. Older students explore how logical reasoning can explain (or fail to explain) counter-intuitive results in Paradoxes and Infinities, or take a more rigorous approach to formal logic in Mathematical Logic.