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His paper was followed by his 1944 book Theory of Games and Economic Behavior co-authored with Oskar Morgenstern.
The true identity of the original correspondent is somewhat elusive given the limited details of the past and the subjective nature of interpretations of what little evidence is available.
Originally, it addressed zero-sum games, in which each participant's gains or losses are exactly balanced by those of the other participants.
Today, game theory applies to a wide range of behavioral relations, and is now an umbrella term for the science of logical decision making in humans, animals, and computers.
Von Neumann's work in game theory culminated in this 1944 book.
This foundational work contains the method for finding mutually consistent solutions for two-person zero-sum games.