Lexicographic probabilities and robustness

Henrik Petri

doi:10.1016/j.geb.2020.05.005

Lexicographic probabilities and robustness

Henrik Petri

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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 x_ω and y_ω 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 language	English
Pages (from-to)	426-439
Number of pages	14
Journal	Games and Economic Behavior
Volume	122
Early online date	1 Jun 2020
DOIs	https://doi.org/10.1016/j.geb.2020.05.005
Publication status	Published - 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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10.1016/j.geb.2020.05.005

LCPS_GEBAccepted author manuscript, 211 KBLicence: CC BY-NC-ND

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AB - 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.

KW - Epistemic game theory

KW - Lexicographic probability systems

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Lexicographic probabilities and robustness

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Keywords

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