Lexicographic beliefs and assumption

Eddie Dekel, Amanda Friedenberg, Marciano Siniscalchi

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

Foundations for iterated admissibility (i.e., the iterated removal of weakly dominated strategies) need to confront a fundamental challenge. On the one hand, admissibility requires that a player consider every strategy of their opponents possible. On the other hand, reasoning that the opponents are rational requires ruling out certain strategies. Brandenburger, Friedenberg, Keisler's (BFK, Econometrica, 2008) foundations for iterated admissibility address this challenge with two ingredients: lexicographic beliefs and the concept of "assumption." However, BFK restrict attention to lexicographic beliefs whose supports are essentially disjoint. This restriction does not have a compelling behavioral rationale, or a clear intuitive interpretation. At the same time, it plays a crucial role in BFK's foundations for iterated admissibility-specifically, in their analysis of assumption. We provide an alternate characterization of assumption, which applies to all lexicographic beliefs. We also characterize two variants of assumption, based on two extensions of 'weak dominance' to infinite state spaces. These notions of assumption coincide with BFK's notion when the state space is finite and lexicographic beliefs have disjoint support; but they are different in more general settings. Leveraging these characterization results, we show that disjoint supports do not play a role in the foundations for iterated admissibility.

Original languageEnglish (US)
Pages (from-to)955-985
Number of pages31
JournalJournal of Economic Theory
Volume163
DOIs
StatePublished - May 1 2016

Keywords

  • Assumption
  • Epistemic game theory
  • Iterated admissibility
  • Lexicographic probability systems
  • Weak dominance
  • Weak dominance in infinite games

ASJC Scopus subject areas

  • Economics and Econometrics

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    Dekel, E., Friedenberg, A., & Siniscalchi, M. (2016). Lexicographic beliefs and assumption. Journal of Economic Theory, 163, 955-985. https://doi.org/10.1016/j.jet.2016.03.003