Theoretical Economics, Volume 9, Number 3 (September 2014)

Theoretical Economics 9 (2014), 779–816

Second order beliefs models of choice under imprecise risk: non-additive second order beliefs vs. nonlinear second order utility

Raphaƫl Giraud


This paper discusses models of choice under imprecise objective probabilistic information featuring beliefs about beliefs -- second order beliefs. A new model, called Second Order Dual Expected Utility (SODEU) featuring non-additive second order beliefs is introduced, axiomatized and systematically contrasted with the leading alternative model of this kind, the Second Order Subjective Expected Utility (SOSEU) model (Klibanoff, Marinacci, Mukerji, 2005; Nau, 2006; Seo, 2009) for which, for the sake of comparison, we provide a new axiomatization, dispensing with the complex constructs used in extant axiomatizations. Ambiguity attitude and attitude toward information in general are discussed and characterized.

Keywords: Imprecise probabilistic information, second order beliefs, non-additive probabilities, ambiguity aversion, Ellsberg paradox, Choquet integral

JEL classification: D81

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