Zur Theorie der Gesellschaftsspiele

Berlin: Julius Springer, 1928. First Edition. Cloth. Near Fine. First Edition. IV, [1]-751, [1] pages. 8vo. Later blue cloth with gilt titling "Mathematische Annalen | 100 | 1928" on spine panel. Upper corner of textblock bumped, otherwise bright and clean internally with just a few pencilled notations. Text in German. Cloth. The first and most important paper by von Neumann related to the Theory of Games, where he establishes his minimax theorem and offers the first general proof. A fundamentally important piece of mathematics that has established and/or significantly enhanced many fields, not the least of which is economics.

"The first proof of the minimax theorem for two-person games of chance and skill with any finite number of pure strategies was given by John von Neumann (1928) in a paper presented to the Gottingen Mathematical Society on 7 December 1926...John von Neumann deserves the credit for the first general proof of the minimax theorem." (Weintraub, pp 24-25)

"...John von Neumann single-handely invented game theory, introducing the genral mathematical concept of 'strategy' in [the present paper which ] contained the proof of his famous '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." OOC 953.

"The role as founder is even more obvious for the theory of games, which von Neumann, in a 1926 paper, conjured - so to speak - out of nowhere...This [minimax theory] was the starting point for far reaching generalizations, including applications to economics, a topic in which von Neumann became interested in as early as 1937 and that he developed in his major treatise written with O[skar] Morenstern, Theory of Games and Economic behavior (1944). These theories have developed into a full-fledged mathematical discipline, attracting many researchers and branching into several types of applications to the social sciences." (DSB 14, p92)

The paper offered here, "Zur Theorie der Gesellschaftsspiele" was presented first at the Society meeting noted above, and then received on July 24, 1927 for initial publication [ as here ] IN [ Article in Mathematische Annalen Bd. 100 1928, pp. 295 - 320.

Literature:
Weintraub, "Toward a History of Game Theory" (which traces the contributions of Borel and others and notes that von Neumann was definitely not working in a vacuum)
Hook and Norman Origins of Cyberspace (#953, discussing von Neumann's joint work with Morgenstern)
Dictionary of Scientific Biography (for more background on von Neumann)
Aspray, John von Neumann and the Origins of Modern Computing, #1928h.