Why forward induction leads to the backward induction outcome: A new proof for Battigalli's theorem

Andrés Perea y Monsuwé*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

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.
Original languageEnglish
Pages (from-to)120-138
Number of pages19
JournalGames and Economic Behavior
Volume110
DOIs
Publication statusPublished - Jul 2018

JEL classifications

  • c72 - Noncooperative Games

Keywords

  • backward induction
  • forward induction
  • extensive-form rationalizability
  • Battigalli's theorem
  • order independence
  • monotonicity
  • Backward induction
  • RATIONALIZABILITY
  • Order independence
  • BEHAVIOR
  • EXTENSIVE GAMES
  • BELIEF
  • Forward induction
  • DOMINANCE
  • EQUILIBRIA
  • PERFECTION
  • Extensive-form rationalizability
  • Monotonicity

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