This text reviews a recent approach to modeling "radically uncertain" behavior in strategic interactions. By rigorously rooting the approach in decision theory, we provide a foundation for applications of Knightian uncertainty in mechanism design, principal agent and moral hazard models. We...

We introduce and analyze three definitions of equilibrium for finite extensive games with imperfect information and ambiguity averse players. In a setting where players' preferences are represented by maxmin expected utility, as characterized in Gilboa and Schmeidler (1989), our definitions...

In this thesis I propose a framework for normal and extensive form games where players can use Knightian uncertainty strategically. In such Ellsberg games, ambiguity-averse players may render their actions objectively ambiguous by using devices such as Ellsberg urns, in addition to the standard...

In classic game theory, agents use mixed strategies in the form of objective and probabilistically precise devices to conceal their actions. We introduce the larger set of probabilistically imprecise devices as strategies and study the consequences for the basic results of normal form games....

We examine repeated Cournot oligopolies when there is uncertainty about the number of players. Already in the static game, such uncertainty can imply outputs above Nash. For the repeated game, we argue that the uncertainty may lead to a novel strategy, based on a notion of limited depth of...

The paper studies when efficient allocations are implementable via coalition-proof mechanisms. When ambiguous mechanisms are allowed and agents are maxmin expected utility maximizers, we prove that all efficient allocations are implementable via interim coalition incentive compatible mechanisms...

A game-theoretic framework that allows for explicitly randomized strategies is used to study the effect of ambiguity aversion on equilibrium outcomes. The notions of "independent strategies" as well as of "common priors" are amended to render them applicable to games in which players lack...

In the standard formulation of game theory, agents use mixed strategies in the form of objective and probabilistically precise devices to conceal their actions. We introduce the larger set of probabilistically imprecise devices and study the consequences for the basic results on normal form...

This paper proposes that the ambiguity reflected by a set of priors remains unchanged when the set is translated within the probability simplex, i.e. ambiguity is location invariant. This unifies and generalises numerous influential definitions of ambiguity in the literature. Location invariance...