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Information order in monotone decision problems under uncertainty

Jian Li and Junjie Zhou

Journal of Economic Theory, 2020, vol. 187, issue C

Abstract: This paper examines the robustness of Lehmann's ranking of experiments (Lehmann, 1988) for decisionmakers who are uncertainty averse à la Cerreia-Vioglio et al. (2011). We show that, assuming commitment, for all uncertainty-averse indices satisfying some mild assumptions, Lehmann's informativeness ranking is equivalent to the induced uncertainty-averse value ranking of experiments for all agents with single-crossing vNM utility indices (Theorem 1). Moreover, Lehmann's ranking can also be detected by varying the uncertainty-averse indices for a fixed finite collection of vNM utility indices (Proposition 1). Our findings suggest that Lehmann's ranking can be a useful enrichment of Blackwell's ranking for monotone decision problems even if ambiguity is present. We apply our results to problems that include social aggregation of information preferences and investment decisions.

Keywords: Informativeness; Ambiguity aversion; Single-crossing property; Monotone comparative statics; Statistical decision theory (search for similar items in EconPapers)
JEL-codes: C44 D81 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.jet.2020.105012

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