Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games1

Additional Material on “Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games”

Strategies and interactive beliefs in dynamic games

Interactive epistemology in dynamic games studies forms of strategic reasoning like backward and forward induction by means of a formal representation of players’ beliefs about each other, conditional on each history. Work on this topic typically relies on epistemic models where states of the world specify both strategies and beliefs. Strategies are conjunctions of behavioral conditionals of th...

Forward Induction, Strong Beliefs, and Unawareness in Dynamic Psychological Games

We provide an epistemic model of dynamic psychological games with unawareness. To formulate epistemic statements, we extend Battigalli and Siniscalchi (1999)’s hierarchies of conditional beliefs by constructing a space of infinite (coherent) hierarchies for each possible awareness level. The interpretation is that only hierarchies of beliefs at the highest awareness level are full descriptions ...

Epistemic equivalence of extended belief hierarchies

In this paper, we introduce a notion of epistemic equivalence between hierarchies of conditional beliefs and hierarchies of lexicographic beliefs, thus extending the standard equivalence results of Halpern (2010) and Brandenburger et al. (2007) to an interactive setting, and we show that there is a Borel surjective function, mapping each conditional belief hierarchy to its epistemically equival...

Hierarchies of ambiguous beliefs

We present a theory of interactive beliefs analogous to Mertens and Zamir [31] and Brandenburger and Dekel [10] that allows for hierarchies of ambiguity. Each agent is allowed a compact set of beliefs at each level, rather than just a single belief as in the standard model. We propose appropriate definitions of coherency and common knowledge for our types. Common knowledge of coherency closes t...