Game theory is a formal language for modeling and analyzing the interactive behaviors of intelligent, rational decision-makers (or players). Game theory provides the mathematical methods necessary to analyze the decisions of two or more players based on their preferences to determine a final outcome. The theory was first conceptualized by mathematician Ernst Zermelo in the early 20th century. However, John von Neumann pioneered modern game theory through his book Theory of Games and Economic Behavior, written alongside co-author Oskar Morgenstern. For this reason, John von Neumann is often credited by historians as the Father of Game Theory. This theory has provided a framework for approaching complex, high-pressure situations and has a broad spectrum of applications. These applications of game theory have helped shape modern economics and social sciences as we know them today and are discussed in the Applications section below.

Analyzing game theoretic situations is a practical application of linear programming. These situations can get quite complex mathematically, but one of the simplest forms of game is called the Finite Two-Person Zero-Sum Game (or Matrix Game for short). In a Matrix Game, two players are involved in a competitive situation in which one player’s loss is the other’s gain. Some common terms related to the Matrix Game that will be used throughout this chapter have been defined below: