A Brief History of Determinacy

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Determinacy axioms are statements to the effect that certain games are deter- mined, in that each player in the game has an optimal strategy.1 The commonly accepted axioms for mathematics, the Zermelo-Fraenkel axioms with the Axiom of Choice (ZFC; see [Jech, 2003; Kunen, 1983]), imply the determinacy of many games that people actually play. This applies in particular to many games of per- fect information, games in which the players alternate moves which are known to both players, and the outcome of the game depends only on this list of moves, and not on chance or other external factors. Games of perfect information which must end in finitely many moves are determined. This follows from the work of Ernst Zermelo [1913], D´enes K˝onig [1927] and L´aszl´o K´almar [1928], and also from the independent work of John von Neumann and Oskar Morgenstern (in their 1944 book, reprinted as [2004]).

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  • Paul B. Larson

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