We define a cautious version of extensive-form rationalizability for generalized extensive-form games with unawareness that we call prudent rationalizability. It is an extensive-form analog of iterated admissibility. In each round of the procedure, for each tree and each information set of a player a surviving strategy of hers is required to be rational vis-a-vis a belief system with a full-support belief on the opponents' previously surviving strategies that reach that information set. We demonstrate the applicability of prudent rationalizability. In games of disclosure of verifiable information, we show that prudent rationalizability yields unraveling under full awareness but unraveling might fail under unawareness. We compare prudent rationalizability to extensive-form rationalizability. We show that prudent rationalizability may not refine extensive-form rationalizability strategies but conjecture that the paths induced by prudent rationalizable strategy profiles (weakly) refine the set of paths induced by extensive-form rationalizable strategies.
Bibliographical noteFunding Information:
Aviad is grateful for financial support from the Open University of Israel's Research Fund grant no. 46106. Martin was supported by the Spanish Ministerio de Educación y Ciencia via a Ramon y Cajal Fellowship (IAE-CSIC) and a Research Grant (SEJ 2006-02079). Burkhard is grateful for financial support from the NSF SES-0647811.
© 2020 Walter de Gruyter GmbH, Berlin/Boston 2020.
- common strong cautious belief in rationality
- extensive-form rationalizability
- iterated admissibility
- persuasion games
- verifiable information