<P> Modern game theory began with the idea regarding the existence of mixed - strategy equilibria in two - person zero - sum games and its proof by John von Neumann . Von Neumann's original proof used the Brouwer fixed - point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics . His paper was followed by the 1944 book Theory of Games and Economic Behavior, co-written with Oskar Morgenstern, which considered cooperative games of several players . The second edition of this book provided an axiomatic theory of expected utility, which allowed mathematical statisticians and economists to treat decision - making under uncertainty . </P> <P> This theory was developed extensively in the 1950s by many scholars . Game theory was later explicitly applied to biology in the 1970s, although similar developments go back at least as far as the 1930s . Game theory has been widely recognized as an important tool in many fields . With the Nobel Memorial Prize in Economic Sciences going to game theorist Jean Tirole in 2014, eleven game - theorists have now won the economics Nobel Prize . John Maynard Smith was awarded the Crafoord Prize for his application of game theory to biology . </P> <P> Early discussions of examples of two - person games occurred long before the rise of modern, mathematical game theory . The first known discussion of game theory occurred in a letter written by Charles Waldegrave, an active Jacobite, and uncle to James Waldegrave, a British diplomat, in 1713 . In this letter, Waldegrave provides a minimax mixed strategy solution to a two - person version of the card game le Her, and the problem is now known as Waldegrave problem . James Madison made what we now recognize as a game - theoretic analysis of the ways states can be expected to behave under different systems of taxation . In his 1838 Recherches sur les principes mathématiques de la théorie des richesses (Researches into the Mathematical Principles of the Theory of Wealth), Antoine Augustin Cournot considered a duopoly and presents a solution that is a restricted version of the Nash equilibrium . </P> <P> In 1913, Ernst Zermelo published Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels (On an Application of Set Theory to the Theory of the Game of Chess). It proved that the optimal chess strategy is strictly determined . This paved the way for more general theorems . </P>

Who gave the concept of game theory first