VON NEUMANN, John. & Oskar MORGENSTERN. Theory of Games and Economic Behavior.
Princeton: Princeton University Press, 1944. First edition, first printing.

The copy of distinguished mathematician Andrew M. Gleason who (together with Montgomery and Zippin) resolved Hilbert’s Fifth Problem; a problem to which Von Neumann also greatly contributed. Gleason’s theorem of mathematical physics plays a fundamental role in quantum mechanics and in particular in hidden variable theories. A fine copy of Von Neumann and Morgenstern's groundbreaking text that created the interdisciplinary research field of game theory. “Quantitative mathematical models for games 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 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 [Zur Theorie der Gesellschaftsspiele, Math. Ann. 100, 1928]. 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 Samuel, Newell, Simon, and others, was more fully articulated and explored in ‘The Theory of Games and Economic Behavior’, co-authored by von Neumann and the Austrian economist Oskar 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. … Von Neumann revolutionized mathematical economics. Had he not suffered an early death from cancer in 1957, he most probably would have received the Noble Prize in economics. Several mathematical economists influenced by von Neumann’s ideas [as Nash, Harsanyi and Selten] later received the Nobel Prize in Economics”. (Hook & Norman: Origins of Cyberspace, p.473). OOC 953 [lacking jacket]; Norman 2167. Provenance: With the stamp of the distinguished American mathematician Andrew Mattei Gleason (1921-2008) famous for contributions in solving Hilbert's Fifth Problem and Gleason's theorem. "Gleason won the Newcomb Cleveland Prize from the American Association for the Advancement of Science [in 1952] for his contribution to the solution of the problem. It was, as was stated when the prize was presented to him ‘... an outstanding contribution to science’.” (MacTutor History of Mathematics). He was elected to the American Academy of Arts and Sciences in 1956, to the National Academy of Science in 1966, and to the American Philosophical Society in 1977. Gleason's solution to Hilbert's problem [the question of whether all continuous groups are automatically differential groups] partly built on the work by Von Neumann in this field, and in particular on Von Neumann’s important 1933 solution of the problem in the special case of compact groups. Gleason’s theorem, on the uniqueness of measures in quantum mechanics, plays a fundamental role in the analysis of quantum measurement, and was essential to the groundbreaking work done in the 1960’s by John Bell on hidden variable theories of quantum physics; also a problem which Von Neumann worked much on.

8vo: 234 x 155 mm. Original cloth without the rare dust jacket; binding tight and clean. Rubberstamp 'Andrew M. Gleason' to the front free end-paper XVIII, 625, (1) pp. Errata sheet loosely inserted, as issued. Completley clean and fresh throughout. A fine copy.