Lexicographic probabilities and robustness

Research output: Contribution to journalArticlepeer-review

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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