Lexicographic probabilities and robustness

Henrik Petri

Games and Economic Behavior, 2020, vol. 122, issue C, 426-439

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.

Keywords: Lexicographic probability systems; Non-Archimedean preferences; Subjective expected utility; Epistemic game theory (search for similar items in EconPapers)
JEL-codes: C65 D11 (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:gamebe:v:122:y:2020:i:c:p:426-439

DOI: 10.1016/j.geb.2020.05.005

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