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.
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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.
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Aumann, R.J., Hart, S. Bi-convexity and bi-martingales. Israel J. Math. 54, 159–180 (1986). https://doi.org/10.1007/BF02764940
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DOI: https://doi.org/10.1007/BF02764940