Game theory is the mathematical study of how players act during a game. The final goal is to provide strategies that optimize the payoffs for all players in the game. Game theory is an important tool in economics, international relations, business management and other fields.  The Wolfram Language provides functionality for studying both simultaneous games and sequential games. This includes dedicated functions for visualizing games, finding and verifying optimal strategies and computing the payoffs for players using a given strategy. A large library of well-known games is available along with their descriptions, sources, etc. to facilitate learning and applications of this important subject.

Matrix or Simultaneous Games

MatrixGame — represents a simultaneous game specified by payoff matrices or arrays

MatrixGamePlot — visualizes a matrix game

FindMatrixGameStrategies — find Nash equilibria etc.

VerifyMatrixGameStrategy — verify that a strategy is a Nash equilibrium etc.

MatrixGamePayoff — give the expected payoff for a strategy profile

Tree or Sequential Games

TreeGame — represents a sequential game specified by a game tree

TreeGamePlot — visualizes a tree game

FindTreeGameStrategies — find subgame perfect equilibria (SPEs) etc.

VerifyTreeGameStrategy — verify that a strategy is an SPE etc.

TreeGamePayoff — give the expected payoff for a strategy profile

Options

GameActionLabels  ▪  GamePlayerLabels

Game Constructors

GameTheoryData — predefined games