Information Structures with Unawareness

Abstract

† I am indebted to Bart Lipman for his invaluable guidance throughout the course of this project. I am grateful to Larry Samuelson and Bill Sandholm for many inspiring discussions and advice, and to Yossi Feinberg and two anonymous referees for helpful comments.

Probabilistic Unawareness

“…7 Once again, the idea is already present in [24]: "...a smaller world is derived from a larger by neglecting some distinctions between states". The idea of capturing unawareness with the help of coarse-grained or subjective state spaces is widely shared in the literature; see, for instance, [8] or [9]. By contrast, in the framework of first-order epistemic logic, unawareness is construed as unawareness of some objects in the domain of interpretation by [25].…”

“…The syntactic framework, in particular, varies from one to another. The logic on which this paper is based relies on a language that is quite similar to that of doxastic logic, and it therefore can be seen as constituting a probabilistic modal logic: its primary doxastic operators are L a , where a is a rational number between zero and one ("the agent believes at least to degree a that...") 9 We can express the relevant intuitive principles for L a as:…”

“…The very same awareness c structures are used to weaken the full awareness assumption. More recently, game theorists have become interested in weakening awareness in epistemic and doxastic logic and in related formalisms ( [5][6][7][8][9][10]) 3 . For a recent and detailed survey of models of unawareness, see [14].…”

Unawareness of theorems

“…In order to overcome the impossibility result of Dekel et al (1998), the paper follows the approach of Heifetz et al (2009) and Li (2009) of introducing multiple state spaces. However, it retains the set-theoretic nature exhibited also in the standard model of knowledge and as a result, familiar notions naturally extend here.…”

“…A new property called Awareness Leads to Knowledge shows that unawareness of theorems not only constrains an agent's knowledge, but also, can impair his reasoning about what other agents know. For example, in contrast to Li (2009), Heifetz et al (2006 and the standard model of knowledge, it is possible that two agents disagree on whether another agent knows a particular event. The model follows Aumann (1976) in defining common knowledge and characterizing it in terms of a self evident event, but departs in showing that no-trade theorems do not hold.…”