This meaning to uncertainty is attributed to Frank Knight, and is sometimes referred to as Knightian uncertainty.
The decisionmaker can apply game theory even in such a circumstance, e.g. the choice of a dominant strategy.
Kreps (1988), p 31, writes that three standard ways of modeling choices made under conditions of uncertainty are with von Neumann-Morgenstern expected utility over objective uncertainty, the Savage axioms for modeling subjective uncertainty, and the Anscombe-Aumann theory which is a middle course between them.
A recent ad for a new book edited by Haim Levy (Stochastic Dominance: Investment Decision Making under Uncertainty) considers three ways of modeling investment choices under uncertainty: by tradeoffs between mean and variance, by choices made by stochastic dominance, and non-expected utility approaches using prospect theory.
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