Backward Induction Reasoning beyond Backward Induction

Emiliano Catonini and Antonio Penta

No 1315, Working Papers from Barcelona School of Economics

Abstract: Backward Induction is a fundamental concept in game theory. As an algorithm, it can only be used to analyze a very narrow class of games, but its logic is also invoked, albeit informally, in several solution concepts for games with imperfect or incomplete information (Subgame Perfect Equilibrium, Sequential Equilibrium, etc.). Yet, the very meaning of ‘backward induction reasoning’ is not clear in these settings, and we lack a way to apply this simple and compelling idea to more general games. We remedy this by introducing a solution concept for games with imperfect and incomplete information, Backwards Rationalizability, that captures precisely the implications of backward induction reasoning. We show that Backwards Rationalizability satisfies several properties that are normally ascribed to backward induction reasoning, such as: (i) an incomplete-information extension of subgame consistency (continuation-game consistency); (ii) the possibility, in finite horizon games, of being computed via a tractable backwards procedure; (iii) the view of unexpected moves as mistakes; (iv) a characterization of the robust predictions of a ‘perfect equilibrium’ notion that introduces the backward induction logic and nothing more into equilibrium analysis. We also discuss a few applications, including a new version of peer-confirming equilibrium (Lipnowski and Sadler (2019)) that, thanks to the backward induction logic distilled by Backwards Rationalizability, restores in dynamic games the natural comparative statics the original concept only displays in static settings.

Keywords: backward induction; backwards procedure; backwards rationalizability; Incomplete Information; interim perfect equilibrium; Rationalizability; robustness (search for similar items in EconPapers)
JEL-codes: C72 C73 D82 (search for similar items in EconPapers)
Date: 2022-02
New Economics Papers: this item is included in nep-gth and nep-mic
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
https://bse.eu/sites/default/files/working_paper_pdfs/1315.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bge:wpaper:1315

Access Statistics for this paper

More papers in Working Papers from Barcelona School of Economics Contact information at EDIRC.
Bibliographic data for series maintained by Bruno Guallar ().