Merging with a set of probability measures: a characterization

Artikel

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).

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Journal: Theoretical Economics ; ISSN: 1555-7561 ; Volume: 10 ; Year: 2015 ; Issue: 2 ; Pages: 411-444 ; New Haven, CT: The Econometric Society

Classification and Topics

• Classification: Wirtschaft ; Noncooperative Games ; Stochastic and Dynamic Games; Evolutionary Games; Repeated Games ; Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
• Subject: Bayesian learning ; weak merging ; conditioning rules ; eventual generation ; frequency-based prior

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Noguchi, Yuichi
• Event: Veröffentlichung
• (who): The Econometric Society
• (where): New Haven, CT
• (when): 2015

Further information

• DOI: doi:10.3982/TE1360
• Handle: http://hdl.handle.net/10419/150254
• Last update: 10.03.2025, 11:41 AM CET