title: A Categorical Characterization of a ①-Iteratively De ned State of Common Knowledge
metadata.name: dc.contributor.author
metadata.value: Tohmé, Fernando
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Caterina, Gianluca
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Gangle, Rocco
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2021-11-29T20:55:49Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2021-11-29T20:55:49Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2021-10
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Tohmé F., Caterina G., Gangle R. A Categorical Characterization of a ①-Iteratively De ned State of Common Knowledge. Contributions to Game Theory and Management, XIV, 329-341.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu31.2021.24
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/33706
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: We present here a novel approach to the analysis of common
  knowledge based on category theory. In particular, we model the global epistemic
  state for a given set of agents through a hierarchy of beliefs represented
  by a presheaf construction. Then, by employing the properties of a
  categorical monad, we prove the existence of a state, obtained in an iterative
  fashion, in which all agents acquire common knowledge of some underlying
  statement. In order to guarantee the existence of a fixed point under certain
  suitable conditions, we make use of the properties entailed by Sergeyev's
  numeral system called grossone, which allows a finer control on the relevant
  structure of the infinitely nested epistemic states.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: https://doi.org/10.21638/11701/spbu31.2021.24
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: en
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Contributions to Game Theory and Management;Volume 14
metadata.lang: -
metadata.name: dc.subject
metadata.value: common knowledge
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: category theory
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: grossone
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: A Categorical Characterization of a ①-Iteratively De ned State of Common Knowledge
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 329-341.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/33706/1/329-341.pdf
resources.format: Adobe PDF
resources.size: 549,62 kB