Game Theory - A Historical Perspective

Some believe that the study of Game Theory began with the works of Daniel Bernoulli. A mathematician born in 1700, Bernoulli is probably best known for his work with the properties and relationships of pressure, density, velocity and fluid flow. Known as “Bernoulli’s Principle,” this work forms the basis of jet engine production and operation today. Pressured by his father to enter the world of commerce, he is also credited with introducing the concepts of expected utility and diminishing returns.

This work in particular can be of use when “pricing” bets or bluffs in no-limit poker.

Others believe the first real mathematical tool to become available to game theorists was “Bayes’ Theorem,” published posthumously in England in the 18th century. Thomas Bayes was born in 1702 and was an ordained minister. His work involved using probabilities as a basis for logical inference. (The author has developed and used artificially intelligent systems based on “Bayes’ Theorem” to trade derivatives in today’s financial markets.)

Yet still others believe that the study of Game Theory began with the publication of Antoine Augustin Cournot’s The Recherches in the early 1800s. The work dealt with the optimization of output as a best dynamic response.

Émile Borel was probably the first to formally define important concepts in the use of strategy in games. Born in 1871 in Saint-Affrique, France, he demonstrated an early penchant for mathematics. In 1909 the Sorbonne created a special chair of “Theory of Functions” which Borel held through 1940. During the years 1921–27 he published several papers on Game Theory and several papers on poker. Important to poker players are his discussions on the concepts of imperfect information, mixed strategies and credibility.

In 1944 Princeton University Press published Theory of Games and Economic Behavior by John von Neumann and Oskar Morgenstern. While not the first work to define certain concepts of strategy in games, it is widely recognized as one that has fostered Game Theory as we know it today.

Also important to poker players is the work of Julia Bowman Robinson. Born in 1919, she discovered her passion for mathematics after a bout with scarlet fever and was the first woman admitted to the Academy of Sciences. For poker players her most important work was An Iterative Method of Solving a Game.

Credited by many as being a primary shepherd of modern Game Theory is John Forbes Nash, Jr. Diagnosed as a paranoid schizophrenic, Nash was long troubled by delusions. This condition, now in remission, became the subject of a popular film. His work earned him 1/3 of the 1994 Nobel Prize in Economic Sciences. Born in the Appalachian town of Bluefield, West 2 1. Introduction to Game Theory in Poker Virginia in 1928, Nash became well known for a 28-page work he did at age 21 which defined his “Nash Equilibrium” concerning strategic behavior in non-cooperative games. Poker players are most drawn to the story that while he was in a bar near Princeton and being goaded into approaching an attractive blond-haired lady, he suddenly shouted and then ran off to complete his work on “The Mathematics of Competition” which is one basis of Game Theory today.