Epistemic Foundation of Decision Making under Ambiguity

In the seminal works, Mukerji (1997) and Ghirardato (2001) explain the notion of ambiguity in terms of incompleteness of what the decision maker (DM) knows and demonstrate that such limitation may lead to a non-additive specification of DM’s beliefs. However, these theories do not relate this issue to well established formal models of knowledge. We show that translating the decision theoretic set-up into epistemic logic may provide more deep insight into understanding of the sources of ambiguity on the one side and establish connection to the existing models of knowledge on the other side. In particular, we present that canonical knowledge systems are very well suited tools for this purposes. Furthermore, we show that DM subjective beliefs are represented by non-additive measures, whenever the knowledge operator and possibility operator disperse.