The New School: History Of Economic Thought (HET) Website
According to HET Game Theory developed as a method for examining economic decision making. The theory was first organized by John von Neumann and Oskar Morgenstern's joint 1944 publication, Theory of Games and Economic Behavior. Game Theory is where decisions about strategy are based on actions of other agents or adversaries.
The theory was updated by John Nash in 1950, with the "Nash Equilibrium." The Nash Equilibrium happens when all players produce the best responses to the actions of other players. According to HET, the concept of the Nash Equilibrium can be traced back to French Economist Augustin Cournot in 1838 The first textbook on game theory was published in 1957 by R. Duncan Luce and Howard Raiffa. In the textbook Luce and Raiffa perfected the "Iterated Elimination of Dominated Stratgies (IEDS) for Strategic Normal Games" and the concept of "Repeated Game." Other game theorists in the 1950s and 1960s were H.W. Kuhn with games with "imperfect information" (i.e. players do not know the previous moves of other players); William Vickery with Auctions; Reinhard Selten with "Subgame Perfect Equilibrium" that uses backward induction; and Lloyd Shapely with the "Shapley Value."
The HET goes on to explain how "Evolutionary game theory" developed later and was designed to explain the results from what appeared to be cooperation between human institutions. Strategist Thomas C. Schelling argued that what appeared to be cooperation of social institutions in settling conflicst are actually maintained with threats of retaliation and punishment. HET then lists Nobel Laureates for Game Theory such as Nash, Selten, and Vickery.