Game-Theoretic Foundations for Probability and Statistics

Author: Experimental Mathematics

Glenn Shafer, Rutgers Business School
Rutgers University Experimental Math Seminar, February 14, 2019
Abstract: Fermat and Pascal’s two different methods for solving the problem of division lead to two different mathematical foundations for probability theory: a measure-theoretic foundation that generalizes the method of counting cases used by Fermat, and a game-theoretic foundation that generalizes the method of backward recursion used by Pascal. The game-theoretic foundation has flourished in recent decades, as documented by my forthcoming book with Vovk, Game-Theoretic Foundations for Probability and Finance. In this book’s formulation, probability typically involves a perfect-information game with three players, a player who offers betting rates (Forecaster), a player who tests the reliability of the forecaster by trying to multiply the capital he risks betting at these rates (Skeptic), and a player who decides the outcomes (Reality).

Video source Vimeo

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