Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/150254
Title:

Merging with a set of probability measures: a characterization

Authors:
Noguchi, Yuichi
Year of Publication:
2015
Citation:
[Journal:] Theoretical Economics [ISSN:] 1555-7561 [Volume:] 10 [Year:] 2015 [Issue:] 2 [Pages:] 411-444
Abstract:
In this paper, I provide a characterization of a \textit{set} of probability measures with which a prior weakly merges.'' In this regard, I introduce the concept of conditioning rules'' that represent the \textit{regularities% } of probability measures and define the eventual generation'' of probability measures by a family of conditioning rules. I then show that a set of probability measures is learnable (i.e., all probability measures in the set are weakly merged by a prior) if and only if all probability measures in the set are eventually generated by a \textit{countable} family of conditioning rules. I also demonstrate that quite similar results are obtained with almost weak merging.'' In addition, I argue that my characterization result can be extended to the case of infinitely repeated games and has some interesting applications with regard to the impossibility result in Nachbar (1997, 2005).
Subjects:
Bayesian learning
weak merging
conditioning rules
eventual generation
frequency-based prior
JEL:
C72
C73
D83
Persistent Identifier of the first edition:
Document Type:
Article
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