You say game theory, others say theory of social interaction. Still others call it weather forecasting, economic predictions, and playing the odds in Vegas. Then there are the people who put game theory to work in evolutionary biology, political science, philosophy, engineering, and the computer sciences. We just might be surrounded by game theory in play, so to speak, without even knowing what it is.
It may sound like fun but game theory is serious business. Nobel prize serious. So far, eight Nobel prizes have been awarded to scientists who based their findings on the way game theory was applied in their field of study, from biology to economics.
The basic concept behind game theory is to capture and predict the behavior of all elements of a strategic situation, be that situation truly fun and games or political games, war or weather, money or manners.
In short, game theory mathematically analyzes strategies used to deal with or predict the outcome of competitive situations, especially situations where one participant (person, player, event, or action) influences the actions of or options for all other participants involved.
It may sound new and intimidating but it isn’t; it’s been around a very long time. In modern times, publication of the book, Theory of Games and Economic Behavior, in 1944 by John von Neumann and Oskar Morgenstern, is considered the benchmark for modern scientific applications but it certainly isn’t the first time in history that game theory was an issue. The Babylonian Talmud, dating to before 500 AD, gives an example of game theory, although not by that name, in a discussion of how to distribute a man’s wealth when he dies and leaves three wives behind.
This timeline probably won’t make those three widows any happier but it may be helpful for gaining a better understanding of how game theory has been used over the years and how it influences so much of life today.
0 - 500 AD
The problem of the three widows is included in the Babylonian Talmud, which is the foundation of Jewish religion as well as its civil and criminal law.
James Waldegrave writes a letter to his friend Pierre-Remond de Montmort describing his strategy for winning a two-player card game called le Her. Montmort describes this strategy to yet another friend as a mixed strategy with unusual rules of play.
Augustin Cournot publishes Researches into the Mathematical Principles of the Theory of Wealth, in which chapter 7 (“On the Competition of Producers”) utilizes a simplified version of what was to become the Nash equilibrium.
Charles Darwin puts game theory to work in his book, The Descent of Man, and Selection in Relation to Sex. In it, game theory is implied but not named in his discussion of how a population produces a functional ratio of male to female offspring.
Francis Ysidro Edgeworth publishes Mathematical Psychics: An Essay on the Application of Mathematics to the Moral Sciences. The subject is prediction of the outcome of trading two commodities with two types of consumer.
Ernst Zermelo publishes the paper, Uber eine Anwendung der Mengenlehre auf die Theorie des Schachspiels, representing the first time the concept is officially described as a theorem. It describes how either white or black can force a win in a game of chess or both sides can force a draw.
1921 - 1927
Emile Borel publishes four papers dealing with strategic games that discuss what is to become the minimax solution, which represents the theory that, in a two-player game, the loser’s smallest maximum loss will be equal to the winner’s greatest possible minimum win. Though presented, Borel was unable to prove his theory at the time.
John von Neumann proved Borel’s minimax theorem.
Problems of Monopoly and Economic Warfare, by F. Zeuthen, proposes a solution to the problem of bargaining.
R. A. Fisher publishes the paper, Randomisation and an Old Enigma of Card Play, which delivers the solution to Waldegrave’s puzzling card-playing strategy.
John von Neumann and Oskar Morgenstern publish their seminal work, Theory of Games and Economic Behavior.
H. Loomis publishes On a Theorem of von Neumann, the first proof of the minimax theory that relies entirely upon algebra.
Strategy in Poker, Business and War, by John McDonald, introduces game theory to the general public.
1950 - 1953
John Nash publishes a series of four papers dealing with bargaining theory and non-cooperative game theory; from them came the Nash program, the Nash bargaining solution, the Nash equilibrium, and the axiomatic bargaining theory.
John Charles C. McKinsey’s Introduction to the Theory of Games becomes the first textbook devoted to game theory.
S. Shapely and M. Shubik bring game theory to political science with their paper, A Method for Evaluating the Distribution of Power in a Committee System.
1954 - 1955
Military pursuit games became the basis for Rufus Isaacs’ Differential Games publications.
Philosophy and game theory collide in R. B. Braithwaite’s Theory of Games as a Tool for the Moral Philosopher.
Evolutionary biology once again connects with game theory in Evolution and the Theory of Games, by R. C. Lewontin.
Romance and intrigue enter the theory of games when D. Gale and L. Shapley ask if it’s possible to match up men and women in such a way that there will be no pair (one man and one woman) that prefers each other over the partners with whom they are already involved. See College Admissions and the Stability of Marriage for complete details.
Application of Game Theory to Some Problems in Automobile Insurance, by Karl Borch, applies game theory to setting insurance premium rates.
Rufus Isaacs publishes Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization.
M. Davis and M. Maschler introduce the Kernel in their work, The Kernel of Cooperative Game.
Oskar Morgenstern debuts the International Journal of Game Theory.
In Games with Randomly Disturbed Payoffs: A New Rationale for Mixed Strategy Equilibrium Points, John Harsanyi theorizes that nobody actually randomizes but the appearance of doing so is the result of unknown payoffs.
G. Faulhaber discusses subsidy-free prices, revenue, and cost allocation in his Cross-Subsidization: Pricing in Public Enterprises.
Robert Aumann’s Agreeing to Disagree formalizes an earlier (1960s) work by D. K. Lewis in which Lewis theorizes that an event becomes common knowledge when all parties know it and all parties know all parties know it and all parties know that all parties know that all parties know it and so on and so forth.
Game theory is the prescription in A. E. Roth’s The Evolution of the Labour Market for Medical Interns and Residents: A Case Study in Game Theory.
The journal, Games and Economic Behavior, is launched.
Douglas G. Baird, Robert H. Gertner, and Randal C.Picker publish Game Theory and the Law, one of the first books to apply game theory specifically and in detail to law and economics.
John Nash wins the Nobel Prize in Economics, along with John C. Harsanyi and Reinhard Selten.
The Nobel for economics goes to Robert J. Aumann and Thomas C. Schelling.
For More Information On Game Theory
Game Theory Open Course - Learn all about game theory from Professor Ben Polak in this open course from Yale University.
Game Theory and Philosophy - The Stanford Encyclopedia of Philosophy has a lot to say about game theory.
John von Neumann - Von Neumann’s theory of games is considered by many mathematicians and scientists to be one of his most original creations.
Game Theory Society - See what the society is doing, who won this year’s council election, and where the 4th World Congress of the Game Theory Society will be held.
What is Game Theory? - Explore the theory from economic and social views.