Lexicographic probabilities and robustness

• 成果类型: Article
• 署名作者: Petri, Henrik
• 署名单位: University of Bath
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2020.05.005
• 发表日期: 2020
• 页码: 426-439
• 关键词: Lexicographic probability systems; Non-Archimedean preferences; subjective expected utility; Epistemic game theory

摘要

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(omega) and y(omega) for some state omega 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. (C) 2020 Elsevier Inc. All rights reserved.