Game-theoretic probability

Vladimir Vovk, Glenn Shafer

Research output: Chapter in Book/Report/Conference proceedingChapter

7 Scopus citations


The standard theory of probability is based on Kolmogorov's measure-theoretic axioms. A less known alternative is the game-theoretic approach to probability. The purpose of this chapter is to give an introduction to the current state of game-theoretic probability. The chapter begins by stating a simple game-theoretic strong law of large numbers. This motivates the introduction of a general discrete-time forecasting protocol and the definition of game-theoretic expectation and probability. The chapter discusses the axiom of continuity for sets of available gambles, and the Doob's argument, which is useful in measure-theoretic and game-theoretic probability. Some limit theorems of game-theoretic probability are also outlined in the chapter. The chapter discusses a different kind of classical results of probability, the zero-one laws, in particular, the Lévy's zero-one law. The last section gives references for further reading.

Original languageEnglish (US)
Title of host publicationIntroduction to Imprecise Probabilities
Number of pages21
ISBN (Electronic)9781118763117
ISBN (Print)9780470973813
StatePublished - Aug 29 2014

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


  • Axiom of continuity
  • Discrete-time forecasting protocol
  • Doob's argument
  • Game-theoretic probability
  • Lévy's zero-one law
  • Measure-theoretic probability
  • Strong law of large numbers


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