Quantitative mathematical models for games such as poker or bridge at one time appeared impossible, since games like these involve free choices by the players at each move, and each move reacts to the moves of other players. However, in the 1920s John von Neumann single-handedly invented game theory, introducing the general mathematical concept of "strategy" in a paper on games of chance (Mathematische Annalen 100  295-320). This contained the proof of his "minimax" theorem that says "a strategy exists that guarantees, for each player, a maximum payoff assuming that the adversary acts so as to minimize that payoff." The "minimax" principle, a key component of the game-playing computer programs developed in the 1950s and 1960s by Arthur Samuel, Allen Newell, Herbert Simon, and others was more fully articulated and explored in The Theory of Games and Economic Behavior, co-authored by von Neumann and Morgenstern.
Game theory, which draws upon mathematical logic, set theory and functional analysis, attempts to describe in mathematical terms the decision-making strategies used in games and other competitive situations. The Von Neumann-Morgenstern theory assumes (1) that people's preferences will remain fixed throughout; (2) that they will have wide knowledge of all available options; (3) that they will be able to calculate their own best interests intelligently; and (4) that they will always act to maximize these interests. Attempts to apply the theory in real-world situations have been problematical, and the theory has been criticized by many, including AI pioneer Herbert Simon, as failing to model the actual decision-making process, which typically takes place in circumstances of relative ignorance where only a limited number of options can be explored.
Von Neumann revolutionized mathematical economics. Had he not suffered an early death from cancer in 1957, most probably he would have received the first Nobel Prize in economics. (The first Nobel prize in economics was awarded in 1969; it cannot be awarded posthumously.) Several mathematical economists influenced by von Neumann's ideas later received the Nobel Prize in economics.
Hook & Norman, Origins of Cyberspace (2002) no. 953.