Acts of Mathematical Creation
Acts of Mathematical Creation
Despite the ex post facto identification of a number of “anticipations” of game-theoretic results through history, it is generally agreed that modern game theory’s founding work was mathematician John von Neumann and economist Oskar Morgenstern’s 1944 book, Theory of Games and Economic Behavior. Yet to a student of game theory trained in recent decades, the book must seem antique in terms of its notations, style of presentation, and terminology. This chapter is therefore principally devoted to explicating the text of von Neumann and Morgenstern’s book, emphasizing the diverse nature of its contents: a dynamic, set-theoretic depiction of games in “extensive form;” the matrix “normal form” of the game and the celebrated “minimax theorem,” with its rich connections to topology and the theory of fixed points; the “characteristic function form” of games and definition of “solutions” as non-dominated sets of imputations; and finally, the von Neumann – Morgenstern theory of utility, which constructed a measure of utility from axioms of preference ordering. These pieces of the theory were not just selectively appropriated and used by different groups of individuals after 1944, but they were also the outgrowth of varied research interests of the book’s authors in the years preceding its publication.
Keywords: John von Neumann, Oskar Morgenstern, Theory of Games and Economic Behavior, extensive form, normal form, set theory, topology, characteristic function, utility
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