Abstract
A set in a product spaceX×Y isbi-convex if all itsx- andy-sections are convex. Abi-martingale is a martingale with values inX×Y whosex- andy-coordinates change only one at a time. This paper investigates the limiting behavior of bimartingales in terms of thebi-convex hull of a set — the smallest bi-convex set containing it — and of several related concepts generalizing the concept of separation to the bi-convex case.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
K. L. Chung,A Course in Probability Theory, Academic Press, New York, 1974.
L. E. Dubins and L. J. Savage,Inequalities for Stochastic Processes: How to Gamble if You Must, Dover, New York, 1976.
S. Hart,Nonzero-sum two-person repeated games with incomplete information, Mathematics of Operations Research10 (1985), 117–153.
P. A. Meyer,Probability and Potentials, Blaisdell Publishing Co., 1966.
T. R. Rockafellar,Convex Analysis, Princeton University Press, 1970.
Author information
Authors and Affiliations
Additional information
Research partially supported by NSF grants at the Institute for Mathematical Studies in the Social Sciences, Standford University. The second author has also been partially supported by the Deutche Forschungsgemeinschaft. We thank Andreu Mas-Colell, Jean-Francois Mertens, Abraham Neyman and Lloyd S. Shapley for many useful discussions.
Rights and permissions
About this article
Cite this article
Aumann, R.J., Hart, S. Bi-convexity and bi-martingales. Israel J. Math. 54, 159–180 (1986). https://doi.org/10.1007/BF02764940
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02764940