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John Nash & Game Theory


Found in: health & phys ed; math, science, 6-8  9-12

John Nash shared the 1994 Nobel Memorial Prize in Economic Science with two other game theorists. Game theory analyzes mathematical models of conflict and cooperation between rational decision-makers. Rather than games in which one player wins and another loses, Nash was interested in non-cooperative games in which all players could gain or lose. His theories have been used in economics, computing, evolutionary biology, artificial intelligence, accounting, politics, and military theory. The New York Times has collected a number of reference articles on the man, his schizophrenia and recovery, and his mathematics under John Forbes Nash Jr.  Nash's struggles with his illness and his recovery became the basis for Sylvia Nasar's biography, A Beautiful Mind, as well as a film of the same name.

Explaining a Cornerstone of Game Theory: John Nash’s Equilibrium critiques a scene from the movie A Beautiful Mind and presents a simpler version of Nash’s Equilibrium in the Prisoner’s Dilemma.

Activities & Games

  • Teacher's Guide: Suggestions for Active Learning features multiple activities in civics, history, economics, and geography for middle school and high school students.
  • Spatial Games are online versions of Hawks versus Doves and Prisoner's Dilemma played on a lattice. Games can be completed in 20-30 minutes.
  • The Game of Hex was invented twice, once in 1942 by Piet Hein, a Danish mathematician and again in 1948 by John Nash. This is a history and description of the two-player strategy game and includes and image of the playing board.
  • Printable Hexboards is a collection of various boards that can be downloaded and printed. Hex can be played by students of all ages.

Background

  • A Brilliant Madness is the companion website for the American Experience program. The website includes an explanation of game theory, a timeline on treatment of mental illness, excerpts (text and video) from an interview with John Nash, a gallery of Nobel prize winners in economics, and a teacher’s guide with activities.
  • American Experience’s A Brilliant Madness: A Mathematical Genius Descent into Madness (2002) (55:04) is available online and may be in local libraries.
  • Unit 9: Game Theory is for high school teachers and can be used to enrich advanced high school math classes. The unit includes a video (28:25) and transcript that introduces game theory, some simpler games, as well as Prisoner’s Dilemma and Hawks and Doves; an interactive, Spatial Games; and support PDFs: textbook unit, facilitator guide and participant guide.
  • ECON 159: Game Theory is an introduction to game theory and strategic thinking. It includes 24 70-minute lectures, problems sets, black board notes, and 2 exams. Lectures 5-8 cover the Nash Equilibrium. This is a college level course and best for professional development and advanced math students.

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