Advanced Search
MyIDEAS: Login

A dynamic epistemic characterization of backward induction without counterfactuals

Contents:

Author Info

  • Bonanno, Giacomo

Abstract

We propose a dynamic framework where the rationality of a playerʼs choice is judged on the basis of the actual beliefs that he has at the time he makes that choice. The set of “possible worlds” is given by state-instant pairs (ω,t), where each state specifies the entire play of the game. At every (ω,t) the beliefs of the active player provide an answer to the question “what will happen if I take action a?”, for every available action a. A player is rational at (ω,t) if either he is not active or the action he takes is optimal given his beliefs. We characterize backward induction in terms of the following event: the first mover (i) is rational and has correct beliefs, (ii) believes that the active player at date 1 is rational and has correct beliefs, (iii) believes that the active player at date 1 believes that the active player at date 2 is rational and has correct beliefs, etc.

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://www.sciencedirect.com/science/article/pii/S0899825612001856
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 78 (2013)
Issue (Month): C ()
Pages: 31-43

as in new window
Handle: RePEc:eee:gamebe:v:78:y:2013:i:c:p:31-43

Contact details of provider:
Web page: http://www.elsevier.com/locate/inca/622836

Related research

Keywords: Perfect-information game; Backward induction; Dynamic interactive beliefs; Rationality; Kripke frame;

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. Ben-Porath, Elchanan, 1997. "Rationality, Nash Equilibrium and Backwards Induction in Perfect-Information Games," Review of Economic Studies, Wiley Blackwell, vol. 64(1), pages 23-46, January.
  2. Adam Brandenburger, 2007. "The power of paradox: some recent developments in interactive epistemology," International Journal of Game Theory, Springer, vol. 35(4), pages 465-492, April.
  3. Dov Samet, 1994. "Hypothetical Knowledge and Games with Perfect Information," Game Theory and Information 9408001, EconWPA, revised 17 Aug 1994.
  4. Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
  5. Giacomo Bonanno & Pierpaolo Battigalli, 2003. "Recent Results On Belief, Knowledge And The Epistemic Foundations Of Game Theory," Working Papers 9814, University of California, Davis, Department of Economics.
  6. Halpern, Joseph Y., 2001. "Substantive Rationality and Backward Induction," Games and Economic Behavior, Elsevier, vol. 37(2), pages 425-435, November.
  7. Stalnaker, Robert, 1996. "Knowledge, Belief and Counterfactual Reasoning in Games," Economics and Philosophy, Cambridge University Press, vol. 12(02), pages 133-163, October.
  8. repec:cup:cbooks:9781107401396 is not listed on IDEAS
  9. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
  10. Balkenborg, Dieter & Eyal Winter, 1995. "A Necessary and Sufficient Epistemic Condition for Playing Backward Induction," Discussion Paper Serie B 331, University of Bonn, Germany.
  11. Perea,Andrés, 2012. "Epistemic Game Theory," Cambridge Books, Cambridge University Press, number 9781107008915, October.
  12. Pierpaolo Battigalli & Alfredo Di Tillio & Dov Samet, 2011. "Strategies and interactive beliefs in dynamic games," Working Papers 375, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
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. Zuazo Gain, Peio, 2014. "Uncertain Information Structures and Backward Induction," IKERLANAK Ikerlanak;2014-79, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.

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:eee:gamebe:v:78:y:2013:i:c:p:31-43. 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: (Zhang, Lei).

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.