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.
Similar content being viewed by others
References
R. J. Aumann,Mixed and behavior strategies in infinite extensive games, Advances in Game Theory, Princeton University Press, Princeton, 1964, pp. 627–650.
D. Blackwell and M. A. Girshick,Theory of Games and Statistical Decisions, Wiley, New York, 1954, Sec. 7.2 and 8.3.
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.
G. Schwarz,Stopping times and martingales, pure and randomized, for games and stochastic processes, submitted to Ann. of Prob.
J. Kelley and I. Namioka,Linear Topological Spaces, Van Nostrand, Princeton, 1963, Sec. 15.
H. W. Kuhn,Extensive games and the problem of information, Ann. Math. Study28, Princeton 1953, pp. 193–216.
J. Neveu,Mathematical Foundations of the Calculus of Probabilities, Holden Day, San Francisco, 1965, Sec. III. 2.
A. Wald and J. Wolfowitz,Two methods of randomization in statistics and the theory of games, Ann. of Math. (2)42 (1951), 581–586.
Author information
Authors and Affiliations
Rights 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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02756820