Lexicographic probabilities and robustness

Research output: Contribution to journalArticle

Abstract

We characterize lexicographic conditional probability systems (LCPSs). Our aim is to address an issue left open in an important contribution by Blume et al. (1991a). They provide a characterization of LCPSs, but one of their axioms quite explicitly imposes disjointness of the supports in an LCPS. The main new axiom is robustness, which is a weak continuity requirement on preferences. It requires preferences between acts x and y to be robust to (unchanged by) small perturbations in payoffs xω and yω for some state ω where x and y are different. LCPSs are characterized as the subclass of lexicographic probability systems satisfying robustness. As a corollary we provide an axiomatization of LCPSs in terms of standard properties satisfied by subjective expected utility preferences (as in Anscombe and Aumann (1963)) and robustness.

Original languageEnglish
Pages (from-to)426-439
Number of pages14
JournalGames and Economic Behavior
Volume122
Early online date1 Jun 2020
DOIs
Publication statusPublished - 31 Jul 2020

Keywords

  • Epistemic game theory
  • Lexicographic probability systems
  • Non-Archimedean preferences
  • Subjective expected utility

ASJC Scopus subject areas

  • Finance
  • Economics and Econometrics

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