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.
|Number of pages||14|
|Journal||Games and Economic Behavior|
|Early online date||1 Jun 2020|
|Publication status||Published - 31 Jul 2020|
- Epistemic game theory
- Lexicographic probability systems
- Non-Archimedean preferences
- Subjective expected utility
ASJC Scopus subject areas
- Economics and Econometrics
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- Department of Economics - Lecturer
- Economic Theory
Person: Research & Teaching