Why forward induction leads to the backward induction outcome: A new proof for Battigalli's theorem
Games and Economic Behavior, 2018, vol. 110, issue C, 120-138
Battigalli (1997) has shown that in dynamic games with perfect information and without relevant ties, the forward induction concept of extensive-form rationalizability yields the backward induction outcome. In this paper we provide a new proof for this remarkable result, based on four steps. We first show that extensive-form rationalizability can be characterized by the iterated application of a special reduction operator, the strong belief reduction operator. We next prove that this operator satisfies a mild version of monotonicity, which we call monotonicity on reachable histories. This property is used to show that for this operator, every possible order of elimination leads to the same set of outcomes. We finally show that backward induction yields a possible order of elimination for the strong belief reduction operator. These four properties together imply Battigalli's theorem.
Keywords: Backward induction; Forward induction; Extensive-form rationalizability; Battigalli's theorem; Order independence; Monotonicity (search for similar items in EconPapers)
JEL-codes: C72 C73 (search for similar items in EconPapers)
References: View references in EconPapers View complete reference list from CitEc
Citations View citations in EconPapers (1) Track citations by RSS feed
Downloads: (external link)
Full text for ScienceDirect subscribers only
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:eee:gamebe:v:110:y:2018:i:c:p:120-138
Access Statistics for this article
Games and Economic Behavior is currently edited by E. Kalai
More articles in Games and Economic Behavior from Elsevier
Bibliographic data for series maintained by Dana Niculescu ().