Transparent Restrictions on Beliefs and Forward Induction Reasoning in Games with Asymmetric Information
AbstractWe analyze forward-induction reasoning in games with asymmetric information assuming some commonly understood restrictions on beliefs. Specifically, we assume that some given restrictions ? on players' initial or conditional first-order beliefs are transparent, that is, not only the restrictions ? hold, but there is common belief in ? at every node. Most applied models of asymmetric information are covered as special cases whereby ? pins down the probabilities initially assigned to states of nature. But the abstract analysis also allows for transparent restrictions on beliefs about behavior, e.g. independence restrictions or restrictions induced by the context behind the game. Our contribution is twofold. First, we use dynamic interactive epistemology to formalize assumptions that capture foward-induction reasoning given the transparency of ?, and show that the behavioral implications of these assumptions are characterized by the ?-rationalizability solution procedure of Battigalli (1999, 2003). Second, we study the differences and similarities between this solution concept and a simpler solution procedure put forward by Battigalli and Siniscalchi (2003). We show that the two procedures are equivalent if ? is "closed under compositions", a property that holds in all the applications considered by Battigalli and Siniscalchi (2003). We also show that when ? is not closed under compositions the simpler solution procedure may fail to characterize the behavioral implications of forward induction reasoning. J.E.L. Classification Numbers: C72, C73, D82. KEYWORDS: Epistemic game theory, Rationalizability, Forward induction, Transparent restrictions on beliefs.
Download InfoIf 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.
Bibliographic InfoPaper provided by IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University in its series Working Papers with number 376.
Date of creation: 2011
Date of revision:
Contact details of provider:
Postal: via Rontgen, 1 - 20136 Milano (Italy)
Web page: http://www.igier.unibocconi.it/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-02-05 (All new papers)
- NEP-CTA-2011-02-05 (Contract Theory & Applications)
- NEP-GTH-2011-02-05 (Game Theory)
You can help add them by filling out this form.
reading list or among the top items on IDEAS.Access and download statisticsgeneral 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: ().
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.