Inception+and+History+of+Game+Theory

The idea of a game mirroring the conflicts of the world is an old one. In the Mabinogion, a collection of Welsh folktales (eleventh to thirteenth centuries), one story has two warring kings playing chess while their armies battle nearby. Each time one king captures a piece, a messenger arrives to inform the other that he has lost a crucial man or division. Finally one king checkmates. A bloody messenger staggers in and tells the loser, "The army is in flight. You have lost the kingdom."

This fiction refers to frankly military origins of chess. The Chinese game of go, the Hindu chaturanga, and many other games are battle simulations, too. Those who see games as simulations of war may see war as a kind of game, too. The classic instance of this was Prussia's century-long infatuation with Kriegspiel. Devised as an educational game for military schools in the eighteenth century, Kriegspiel was originally played on a board consisting on a map of the French-Belgian frontier divided into a grid of 3,600 squares. Game pieces advanced and retreated across the board like armies.

In Budapest, the young John von Neumann played an improvise Kriegspiel with his brothers. During the World War I, John obtained maps of the fronts and followed reports of real advances and retreats. To some critics, game theory is the twentieth century's Kriegspiel, a mirror in which military strategists see reflected their own preconceptions. Game theory is not about "playing" as usually understood. It is about conflict among rational but distrusting beings. Von Neumann escaped revolution and terrorism in Hungary and later the rise of Nazism. His relationship with Klara was one of the repeated conflict. In his letters to his wife John talks of double-crossing, reprisals, and boundless distrust; that's part of what theory game is about. Game theory is a rigorously mathematical study which evolves natural from a reasonable way of looking at conflict. Von Neumann would not have pursued game theory had his mathematical intuition not told him that it was a file gripe for development.

Von Neumann cannot be given undivided credit for the intervention of game theory. Beginning in 1921, seven years before Neumann's first paper, French mathematician Émile Borel published several papers on "la théorie du jeu". The parallels between these paperas and Neumann's work are strong. Borel appreciated the potential economic and military applications of game theory; nevertheless John von Neumann and Oskar Morgenstern are formally credited as the fathers of modern game theory. Their classic book Theory of Games and Economic Behavior (1944) summarises the basic concepts existing at that time. GT has since enjoyed an explosion of developments, including the concept of equilibrium (Nash, 1950), games with imperfect information (Kuhn, 1953), cooperative games (Aumann, 1959, Shubik, 1962), and auctions (Vickrey, 1961), to name just a few. In 1970s GT as a way of analysing strategic situations began to be applied in all sorts of diverse areas including economics, politics, international rela- tions, business and biology. Citing Shubik (2002), “In the 50s ... game theory was looked upon as a curiosum not to be taken seriously by any behavioural scientist. By the late 1980s, game theory in the new industrial organisation has taken over: game theory has proved its success in many disciplines.”

//__References__// Borel, E. (1921), “La theorie du jeu les equations integrales a noyau symetrique”, Comptes Rendus de l’Academie 173; English translation by Savage, L (1953), “The theory of play and integral equations with skew symmetric kernels”, Econometrica, 21.

von Neumann J, Morgenstern O (1944) Theory of games and economic behaviour. Princeton University Press

Nash JF (1950) Equilibrium points in n-person games. Proc Nat Acad Sci USA 36, 48–49

Kuhn HW (1953) Extensive games and the problem of information. In Contributions to the theory of games, vol II, Kuhn HW, Tucker AW, editors. Princeton University Press. 193–216

Aumann RJ (1959) Acceptable points in general cooperative n-person games. In Contributions to the theory of games, vol IV, Kuhn HW, Tucker AW, editors. Princeton University Press. 287–324

Shubik M (1962) Incentives, decentralized control, the assignment of joint costs and internal pricing. Manag Sci 8:325–343

Poundstone, William. 1992. Prisoner’s Dilemma. New York: Doubleday.

Shubik M (2002) Game theory and operations research: some musings 50 years later. Oper Res 50:192–196