Introduction

Game theory is a branch of applied mathematics that uses models to study interactions with formalized incentive structures (“games”). It studies the mathematical models of conflict and cooperation among intelligent and rational decision makers. “Rational” means that each individual's decision-making behavior is consistent with the maximization of subjective expected utility. “Intelligent” means that each individual understands everything about the structure of the situation, including the fact that others are intelligent, rational, decision makers. It has applications in a variety of fields, including economics, international relations, evolutionary biology, political science, and military strategy. Game theorists study predicted and actual behavior, as well as optimal strategies, of individuals in games.

For the history of game theory, the basis of modern game theory can be considered an outgrowth of a few seminal works:

• Augustin Cournot, in his 1838 paper Researches into the Mathematical Principles of the Theory of Wealth, gives an intuitive explanation of what would eventually be formalized as the Nash equilibrium, as well as provides an evolutionary or dynamic notion of best responses to the actions of others.

• Francis Ysidro Edgeworth's Mathematical Physics (1881) demonstrated the notion of competitive equilibriums in a two-person (as well as two-type) economy.

• Emile Borel, in Algebre et calcul des probabilites, Comptes Rendus Academie des Sciences, Vol. 184, 1927, provided the first insight into mixed strategies that state that randomization may support a stable outcome.

Although many other contributors hold a place in the history of game theory, it is widely accepted that modern analysis began with John von Neumann's and Oskar Morgenstern's book, Theory of Games and Economic Behavior, which is the analytical base for the works [217] of John Nash.