For a survey of this literature of Knightian uncertainty/ambiguity, see Gilboa, I., and M. Marinacci, “Ambiguity and the Bayesian Paradigm”, mimeo., April 12, 2011.
12  For reference, please see (1) Nishimura, K.G., and H. Ozaki, “Search and Knightian Uncertainty”, Journal of Economic Theory, 119 (2004), 299–333.and (2) Nishimura, K.G., and H. Ozaki, “Irreversible Investment and Knightian Uncertainty,” Journal of Economic Theory, 136 (2007), 668–694.