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Lexicographic probabilities and robustness

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  • Petri, Henrik

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.

Suggested Citation

  • Petri, Henrik, 2020. "Lexicographic probabilities and robustness," Games and Economic Behavior, Elsevier, vol. 122(C), pages 426-439.
    • Handle: RePEc:eee:gamebe:v:122:y:2020:i:c:p:426-439
    DOI: 10.1016/j.geb.2020.05.005
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    References listed on IDEAS

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    More about this item

    Keywords

    Lexicographic probability systems; Non-Archimedean preferences; Subjective expected utility; Epistemic game theory;
    All these keywords.

    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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