Skip to main content
Log in

Ways of randomizing and the problem of their equivalence

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

Different ways of randomizing have been compared by various authors. An apparent discrepancy between the results stated by game theorists and those stated by statisticians is clarified here, and Kuhn’s theorem on the necessity of perfect recall for the equivalence of two ways of randomizing is extended beyond countable cases.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R. J. Aumann,Mixed and behavior strategies in infinite extensive games, Advances in Game Theory, Princeton University Press, Princeton, 1964, pp. 627–650.

    Google Scholar 

  2. D. Blackwell and M. A. Girshick,Theory of Games and Statistical Decisions, Wiley, New York, 1954, Sec. 7.2 and 8.3.

    MATH  Google Scholar 

  3. L. Dubins and G. Schwarz,On extremal martingale distributions, Proc. Fifth Berkeley Symp. Math. Statist. and Prob. Vol. II/1, Univ. Calif. Press, Berkeley, 1966, pp. 295–299.

    Google Scholar 

  4. G. Schwarz,Stopping times and martingales, pure and randomized, for games and stochastic processes, submitted to Ann. of Prob.

  5. J. Kelley and I. Namioka,Linear Topological Spaces, Van Nostrand, Princeton, 1963, Sec. 15.

    MATH  Google Scholar 

  6. H. W. Kuhn,Extensive games and the problem of information, Ann. Math. Study28, Princeton 1953, pp. 193–216.

    MathSciNet  Google Scholar 

  7. J. Neveu,Mathematical Foundations of the Calculus of Probabilities, Holden Day, San Francisco, 1965, Sec. III. 2.

    Google Scholar 

  8. A. Wald and J. Wolfowitz,Two methods of randomization in statistics and the theory of games, Ann. of Math. (2)42 (1951), 581–586.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schwarz, G. Ways of randomizing and the problem of their equivalence. Israel J. Math. 17, 1–10 (1974). https://doi.org/10.1007/BF02756820

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02756820

Keywords

Navigation