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This thesis contributes to the theoretical work on decision and game theory when decision makers or players perceive ambiguity. The first article introduces a new axiomatic framework for ambiguity aversion and provides axiomatic characterizations for important preference classes that thus far had lacked characterizations. The second article introduces a new axiom called Weak Monotonicity which is shown to play a crucial role in the multiple prior model. It is shown that for many important preference classes, the assumption of monotonic preferences is a consequence of the other axioms and does not have to be assumed. The third article introduces an intuitive definition of perceived ambiguity in the multiple prior model. It is shown that the approach allows an application to games where players perceive strategic ambiguity. A very general equilibrium existence result is given. The modelling capabilities of the approach are highlighted through the analysis of examples. The fourth article applies the model from the previous article to a specific class of games with a lattice-structure. We perform comparative statics on perceived ambiguity and ambiguity attitude. We show that more optimism does not necessarily lead to higher equilibria when players have Alpha-Maxmin preferences. We present necessary and sufficient conditions on the structure of the prior sets for this comparative statics result to hold. The introductory chapter provides the basis of the four articles in this thesis. An overview of axiomatic decision theory, decision-making under ambiguity and ambiguous games is given. It introduces and discusses the most relevant results from the literature.