Advanced Search
MyIDEAS: Login

'Knowing Whether', 'Knowing That' and the Cardinality of State Spaces

Contents:

Author Info

  • Sergiu Hart

    (The Hebrew Uni.)

  • Aviad Heifetz

    (Tel Aviv Uni.)

  • Dov Samet

    (kTel Aviv Uni.)

Abstract

We introduce a new operator on information structures which we call `knowing whether' as opposed to the standard knowledge operator which may be called `knowing that'. The difference between these operators is simple. Saying that an agent knows t h a t a certain event occurred implies that this event indeed occurred, while saying that the agent knows w h e t h e r an event occurred does not imply that the event occurred. (Formally, knowing whether X means that either it is known that X occurred or it is known that X did not occur.) We show that iterating `knowing whether' operators of different agents has a remarkable property that iterations of `knowing that' do not have. When we generate a sequence of events, starting with a given event and then applying `knowing that' or `not knowing that' to the previous event, then the events in this sequence may be, somewhat surprisingly, contradictory. In contrast, any sequence of this type, generated with `knowing whether' and `not knowing whether' is never contradictory. We use this property of the `knowing whether' operator to construct a simple and natural state space and information structures for two agents, such that: (1) any two states are distinct relative to some interactive knowledge of a fixed event, (2) the space has the cardinality of the continuum. This result --- originally proved in a complicated manner by Aumann (1989) --- demonstrates the usefulness of the `knowing whether'

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://128.118.178.162/eps/game/papers/9404/9404002.pdf
Download Restriction: no

File URL: http://128.118.178.162/eps/game/papers/9404/9404002.ps.gz
Download Restriction: no

Bibliographic Info

Paper provided by EconWPA in its series Game Theory and Information with number 9404002.

as in new window
Length: 11 pages
Date of creation: 10 Apr 1994
Date of revision:
Handle: RePEc:wpa:wuwpga:9404002

Note: Plain TeX, 11 pages.
Contact details of provider:
Web page: http://128.118.178.162

Related research

Keywords:

Other versions of this item:

Find related papers by JEL classification:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer, vol. 28(3), pages 263-300.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
  2. Simon Grant & John Quiggin, 2005. "Learning and Discovery," Risk & Uncertainty Working Papers WP7R05, Risk and Sustainable Management Group, University of Queensland.
  3. HEIFETZ, Aviad & MEIER, Martin & SCHIPPER, Burkhard C., 2004. "Interactive unawareness," CORE Discussion Papers 2004059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Koessler, Frederic, 2003. "Persuasion games with higher-order uncertainty," Journal of Economic Theory, Elsevier, vol. 110(2), pages 393-399, June.
  5. Moscati Ivan, 2009. "Interactive and common knowledge in the state-space model," CESMEP Working Papers 200903, University of Turin.
  6. Ehud Lehrer & Dov Samet, 2003. "Agreeing to agree," Game Theory and Information 0310005, EconWPA.
  7. Aviad Heifetz & Martin Meier & Burkhard C. Schipper, 2003. "Interactive Unawareness and Speculative Trade," Bonn Econ Discussion Papers bgse17_2003, University of Bonn, Germany.
  8. Gossner, Olivier & Tsakas, Elias, 2007. "Testing Rationality on Primitive Knowledge," Working Papers in Economics 275, University of Gothenburg, Department of Economics.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpga:9404002. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.