IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this paper

Should I remember more than you? - On the best response to factor-based strategies -

Listed author(s):
  • René Levínský


    (Max Planck Institute of Economics, Jena)

  • Abraham Neyman

    (Institute of Mathematics and Center for the Study of Rationality, The Hebrew University of Jerusalem)

  • Miroslav Zelený

    (Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University)

In this paper we offer a new approach to modeling strategies of bounded complexity, the so-called factor-based strategies. In our model, the strategy of a player in the multi-stage game does not directly map the set of histories to the set of her actions. Instead, the player's perception of is represented by a factor : -> where reflects the "cognitive complexity" of the player. Formally, mapping sends each history to an element of a factor space that represents its equivalence class. The play of the player can then be conditioned just on the elements of the set From the perspective of the original multi-stage game we say that a function from o is a factor of a strategy if there exists a function from to the set of actions of the player such that = In this case we say that the strategy is -factor-asedStationary strategies and strategies played by finite automata and strategies with bounded recall are the most prominent examples of factor-based strategies. In the discounted infinitely repeated game with perfect monitoring, a best reply to a profile of -factor-base strategies need not be a -factor-base strategy. However, if the factor is recursive, namely its value (1 , . . . , ) on a finite string of action profiles ( , . . . , ) is a function of (1 , . . . , - ) and , then for every profile of factor-based strategies there is a best reply that is a pure factor-based strategy. We also study factor-based strategies in the more general case of stochastic games.

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:
Download Restriction: no

Paper provided by Friedrich-Schiller-University Jena in its series Jena Economic Research Papers with number 2010-082.

in new window

Date of creation: 01 Dec 2010
Handle: RePEc:jrp:jrpwrp:2010-082
Contact details of provider: Postal:
Carl-Zeiss-Strasse 3, 07743 JENA

Phone: +049 3641/ 9 43000
Fax: +049 3641/ 9 43000
Web page:

More information through EDIRC

No references listed on IDEAS
You can help add them by filling out this form.

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

When requesting a correction, please mention this item's handle: RePEc:jrp:jrpwrp:2010-082. 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: (Markus Pasche)

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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.