Ambiguity refers to the common situation that the exact probability distribution over events relevant to a decision maker is not objectively known. The Bayesian approach to decision making under ambiguity holds that, nevertheless, all uncertainty can be quantified by a subjective probability distribution and that behavior can be modelled as the maximization of expected utility relative to such a distribution. While the resulting subjective expected utility (SEU) model still reigns supreme in economics, it makes it impossible to study how the presence of ambiguity affects the outcome of economic interactions. To address this concern, recent work on strategic communication and mechanism design has considered the maxmin expected utility (MEU) model of decision making under ambiguity. The MEU model has well-understood axiomatic foundations and is analytically convenient, but is unduly restrictive in that only a ``worst-case scenario'' (obtained by minimizing expected utility over a set of probability distributions) matters for the evaluation of a decision.

A natural response to the restrictiveness of the MEU model is to consider the more general alpha-MEU model. In this model, as originally proposed by Hurwicz in the context of decision making under ignorance, decision are evaluated by a convex combination of their performance (here given by the expected utility) under a worst-case and a best-case scenarios. The primary objective of the project is to investigate the class of Hurwicz preferences, i.e., preferences having such a representation. More specifically, we aim to extend existing work on the axiomatic characterization of Hurwicz preferences and to investigate the strategic use of intentional ambiguity by a principal when agents have such preferences.

For our axiomatic investigations we will work mostly within the well-established Anscombe-Aumann framework. In this setting, the current state of the literature suggests three promising routes to establish axiomatizations for (specific classes of) Hurwicz preferences. The first is to work within the Choquet expected utility (CEU) model in which the structural conditions on capacities that are necessary and sufficient for an alpha-MEU representation are well-known but have, so far, not been translated successfully into corresponding conditions on preferences. The second is to enrich the Anscombe-Aumann framework by positing that there is an objective, but ambiguous, description of the uncertainty faced by the decision maker (as it is common in experimental settings). The third is to abandon the ``purely behavioral'' approach pursued in much of decision theory and relate preferences to a model of the decison making process. We intend to pursue all three of these approaches. The expected results are novel axiomatizations for Hurwicz preferences, providing better foundations for the alpha-MEU model.

The existing literature on the design of ambiguous mechanisms indicates that intentional ambiguity is a very powerful tool to affect the behavior of ambiguity-averse decision makers. The exact role of the assumption of ambiguity aversion for such results is, however, unclear. The purpose of the applied part of the project is gain a better understanding of this issue. The alpha-MEU model is well-suited to do so, because the parameter alpha provides a convenient way to explore the effects of moving away from the extreme case of ambiguity aversion described by the MEU model. While the question motivating this part of a project is a general one, the most obvious starting point for addressing it is the familiar environment of a standard principal-agent problem. In this setting we expect to be able to characterize the best ambiguous mechanism as a function of the parameter alpha and, in particular, identify the conditions under which an ambiguous mechanism cannot improve on the standard solution the principal's problem.