game theory

Table of Contents

Introduction
Classification of games
One-person games
Two-person constant-sum games
- Games of perfect information
- Games of imperfect information
- Mixed strategies and the minimax theorem
- Utility theory
Two-person variable-sum games
- Cooperative versus noncooperative games
- The Nash solution
- The prisoner’s dilemma
  - Theory of moves
  - Biological applications
N-person games
- Sequential and simultaneous truels
- Power in voting: the paradox of the chair’s position
- The von Neumann–Morgenstern theory
- The Banzhaf value in voting games

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payoff matrix with saddlepoint

payoff matrix without saddlepoint

variable-sum payoff matrix

prisoner's dilemma

biological competition

first reduction table

second reduction table

prisoner's dilemma in game theory

See how game theory applies to the peacock's tail evolution

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Topics

incentive compatibility positive-sum game prisoner’s dilemma cooperative game von Neumann-Morgenstern theory utility theory mini-max theorem negative-sum game constant-sum game noncooperative game control theory mathematical programming

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Key People

John von Neumann

John von Neumann

American mathematician

Riker, William

William Riker

American political scientist

Thomas C. Schelling

American economist and game theorist

John Nash

John Nash

American mathematician

Lloyd Shapley, 2012.

Lloyd Shapley

American mathematician

Émile Borel

French mathematician

Alvin E. Roth.

Alvin E. Roth

American economist

Aumann, Robert J.

Robert J. Aumann

Israeli mathematician

Blackwell, David

David Blackwell

American statistician and mathematician

John C. Harsanyi

American economist

Selten, Reinhard

Reinhard Selten

German mathematician

Richard E. Stearns

American mathematician and computer scientist

R.B. Braithwaite

British philosopher

Oskar Morgenstern

German-American economist