Of Game Theory

                     The mathmatical modeling of strategic interaction between rational decision makers is referred to as game theory.  In 1713 in a letter written by Charles Waldegrave he analyzed different strategies for the two person version of the card game le Her and he wrote this letter to his uncle and French diplomat James Waldegrave.  Eventually, these set of strategies for the two person card game became known as the Waldegrave Problem and the letter was the first known conversation about Game Theory.  Former U.S president James Madison made a model of the possible behaviors of states under varoious systems of taxation.  This model would become recognized a game theory model.  In 1838, French philosopher and mathmatician,  Antoine Augustin Cournot published a book titled, "Researches into the Mathematical Principles of the Theory of Wealth".  However, Cournot's work provides a model that is a limited version of John Nash's later equilibrium.  German logician and mathmatician  Ernst Zermelo published a book titled, "On an Application of Set Theory to the Theory of the Game of Chess" in 1913.  This book lead to more in depth analysis of strategic interaction.  Danish economist Fredik Zeuthen found that the mathmatical model is a winning strategy by utilizing Brouwer's fixed point theorem.  In 1938, French mathmatician and politician, Émile Borel published a book titled, "Applications [of probability theory] To Games of Chance; Professed Course at the Faculty of Sciences of Paris".  In this book Borel developed a minimax theorem for two-person zero-sum matrix games only when the pay-off matrix was symmetric.  Borel also proposed that that non-existence of mixed-strategy equilibria in two-person zero-sum games would occur.  However, this idea was later found to be incorrect.
                    In 1928 game theory emerged as a distinct field of study when Hungarian-American mathmatician, physicist, computer scientist, and polymath John von Neumann published a paper titled, "On the Theory of Games of Strategy".  In this paper Von Neumann's original proof utilized Brouwer's fixed-point theorem on continuous mappings into compact convex sets. Thus, this become a standard method in game theory and mathematical economics.  In 1944 Von Neumann published a book titled,  "Theory of Games and Economic Behavior" which he co-authored with Oskar Morgenstern.  In the second edition of this book, Von Beumann proposed  an axiomatic theory of utility, which revived Daniel Bernoulli's archaic theory of utility (of the money) as a seperate field of study.  Also, Von Neumann's 1944 book was the culmination of his research into game theory.  This elementary literature consists of a way to find  mutually consistent solutions for two-person zero-sum games.  Throughout the 1950's research into game theory primarily focused on cooperative game theory in which some of the parties involved in the strategic interaction would mutually agree to follow a certain strategy.  Also, the agreement between these parties were assumed to enforceable.
                       In 1950, a mathmatical model of the prisoner's dilema was developed, and an experiment was performed by exceptional mathmaticians Merrill M Flood and Melvin Dresher, as a portion of the RAND campany's research into game theory. RAND did research into game theory because of its possible application to the arms race between the Soviet Union and the U.S.  During this time period, American mathmatician, John Nash developed a criteria  for mutual consistency of players' strategies applicable to a wider variety of games than the criterion proposed by von Neumann and Morgenstern.  Also,  Nash found that every n-player, non-zero-sum (not just 2-player zero-sum) non-cooperative game has this model.  This model became known as the Nash Equilibrium.  During the 1950's research into game theory increased dramatically as the U.S government hired game theorist to help them understand the strategic interaction between the U.S and the Soviet Union.  Also, the ideas of the core, the extensive form game, fictitious play, repeated games, and the Shapley value were developed.  In Addition, game theory was starting to be applied to philosophy and political science during this era.
                 In 1979, American political scientist Robert Axelrod attempted to set up computer programs as players and found that in tournaments between them the winner was often a basic "tit-for-tat" program that works together on the first step, then in later stages just does whatever its opponent did on the last step. The same winner was also usually obtained by natural selection; a fact widely taken to explain cooperation phenomena in evolutionary biology and the social sciences.  In the 1970's, the research of British thereotical and mathmatical evolutionary biologist and geneticist John Maynard Smith and his  evolutionarily stable strategy led to game theory to be deeply applied to biology especially evolution.  Today game theory techniques are used by many social scientist, biologist, and economist to model strategic interaction between people, organizations, and even, in the case of biologists, animals.  Game theory can be applied to any situation involved strategy.

References

"Game Theory"

https://en.wikipedia.org/wiki/Game_theory